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authorKarl Berry <karl@freefriends.org>2006-01-09 00:49:07 +0000
committerKarl Berry <karl@freefriends.org>2006-01-09 00:49:07 +0000
commit007f67a693e4d031fd3d792df8e4d5f43e2cb2e7 (patch)
tree90d17e00e572ecb1e24764b6f29c80e098b08d29 /Master/texmf-dist/doc/latex/pbsheet
parent950209b26f70aa87ed07c54f82a95b6f03b7c3a0 (diff)
doc/latex
git-svn-id: svn://tug.org/texlive/trunk@84 c570f23f-e606-0410-a88d-b1316a301751
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-rw-r--r--Master/texmf-dist/doc/latex/pbsheet/LPPL318
-rw-r--r--Master/texmf-dist/doc/latex/pbsheet/README61
-rw-r--r--Master/texmf-dist/doc/latex/pbsheet/pbsheet.pdf1629
-rw-r--r--Master/texmf-dist/doc/latex/pbsheet/pbsheet.ps3360
-rw-r--r--Master/texmf-dist/doc/latex/pbsheet/xpl/GNUmakefile85
-rw-r--r--Master/texmf-dist/doc/latex/pbsheet/xpl/img/simbin.eps2459
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-rw-r--r--Master/texmf-dist/doc/latex/pbsheet/xpl/pbsheet.cls551
-rw-r--r--Master/texmf-dist/doc/latex/pbsheet/xpl/pgm/probadis.m65
-rw-r--r--Master/texmf-dist/doc/latex/pbsheet/xpl/pgm/rdiscr.m72
-rw-r--r--Master/texmf-dist/doc/latex/pbsheet/xpl/pgm/rint.m25
-rw-r--r--Master/texmf-dist/doc/latex/pbsheet/xpl/pgm/simbin.m55
-rw-r--r--Master/texmf-dist/doc/latex/pbsheet/xpl/xpl-fr.bib39
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diff --git a/Master/texmf-dist/doc/latex/pbsheet/LPPL b/Master/texmf-dist/doc/latex/pbsheet/LPPL
new file mode 100644
index 00000000000..5b05fe86893
--- /dev/null
+++ b/Master/texmf-dist/doc/latex/pbsheet/LPPL
@@ -0,0 +1,318 @@
+
+The LaTeX Project Public License
+=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
+
+LPPL Version 1.2 1999-09-03
+
+Copyright 1999 LaTeX3 Project
+ Everyone is allowed to distribute verbatim copies of this
+ license document, but modification of it is not allowed.
+
+
+PREAMBLE
+========
+
+The LaTeX Project Public License (LPPL) is the license under which the
+base LaTeX distribution is distributed.
+
+You may use this license for any program that you have written and wish
+to distribute. This license may be particularly suitable if your
+program is TeX-related (such as a LaTeX package), but you may use it
+even if your program is unrelated to TeX. The section `WHETHER AND HOW
+TO DISTRIBUTE PROGRAMS UNDER THIS LICENSE', below, gives instructions,
+examples, and recommendations for authors who are considering
+distributing their programs under this license.
+
+In this license document, `The Program' refers to any program
+distributed under this license.
+
+This license gives conditions under which The Program may be distributed
+and conditions under which modified versions of The Program may be
+distributed. Individual files of The Program may bear supplementary
+and/or superseding conditions on modification of themselves and on the
+distribution of modified versions of themselves, but *no* file of The
+Program may bear supplementary or superseding conditions on the
+distribution of an unmodified copy of the file. A distributor wishing
+to distribute a complete, unmodified copy of The Program therefore
+needs to check the conditions only in this license and nowhere else.
+
+Activities other than distribution and/or modification of The Program
+are not covered by this license; they are outside its scope. In
+particular, the act of running The Program is not restricted.
+
+We, the LaTeX3 Project, believe that the conditions below give you
+the freedom to make and distribute modified versions of The Program
+that conform with whatever technical specifications you wish while
+maintaining the availability, integrity, and reliability of
+The Program. If you do not see how to achieve your goal while
+meeting these conditions, then read the document `cfgguide.tex'
+in the base LaTeX distribution for suggestions.
+
+
+CONDITIONS ON DISTRIBUTION AND MODIFICATION
+===========================================
+
+You may distribute a complete, unmodified copy of The Program.
+Distribution of only part of The Program is not allowed.
+
+You may not modify in any way a file of The Program that bears a legal
+notice forbidding modification of that file.
+
+You may distribute a modified file of The Program if, and only if, the
+following eight conditions are met:
+
+ 1. You must meet any additional conditions borne by the file on the
+ distribution of a modified version of the file as described below
+ in the subsection `Additional Conditions on Individual Files of
+ The Program'.
+
+ 2. If the file is a LaTeX software file, then you must meet any
+ applicable additional conditions on the distribution of a modified
+ version of the file that are described below in the subsection
+ `Additional Conditions on LaTeX Software Files'.
+
+ 3. You must not distribute the modified file with the filename of the
+ original file.
+
+ 4. In the modified file, you must acknowledge the authorship and
+ name of the original file, and the name (if any) of the program
+ which contains it.
+
+ 5. You must change any identification string in the file to indicate
+ clearly that the modified file is not part of The Program.
+
+ 6. You must change any addresses in the modified file for the
+ reporting of errors in the file or in The Program generally to
+ ensure that reports for files no longer maintained by the original
+ maintainers will be directed to the maintainers of the modified
+ files.
+
+ 7. You must distribute the modified file under a license that forbids
+ distribution both of the modified file and of any files derived
+ from the modified file with the filename of the original file.
+
+ 8. You must do either (A) or (B):
+
+ (A) distribute a copy of The Program (that is, a complete,
+ unmodified copy of The Program) together with the modified
+ file; if your distribution of the modified file is made by
+ offering access to copy the modified file from a designated
+ place, then offering equivalent access to copy The Program
+ from the same place meets this condition, even though third
+ parties are not compelled to copy The Program along with the
+ modified file;
+
+ (B) provide to those who receive the modified file information
+ that is sufficient for them to obtain a copy of The Program;
+ for example, you may provide a Uniform Resource Locator (URL)
+ for a site that you expect will provide them with a copy of
+ The Program free of charge (either the version from which
+ your modification is derived, or perhaps a later version).
+
+Note that in the above, `distribution' of a file means making the
+file available to others by any means. This includes, for instance,
+installing the file on any machine in such a way that the file is
+accessible by users other than yourself. `Modification' of a file
+means any procedure that produces a derivative file under any
+applicable law -- that is, a file containing the original file or
+a significant portion of it, either verbatim or with modifications
+and/or translated into another language.
+
+Changing the name of a file (other than as necessitated by the file
+conventions of the target file systems) is considered to be a
+modification of the file.
+
+The distribution conditions in this license do not have to be
+applied to files that have been modified in accordance with the
+above conditions. Note, however, that Condition 7. does apply to
+any such modified file.
+
+The conditions above are not intended to prohibit, and hence do not
+apply to, the updating, by any method, of a file so that it becomes
+identical to the latest version of that file of The Program.
+
+
+
+A Recommendation on Modification Without Distribution
+-----------------------------------------------------
+
+It is wise never to modify a file of The Program, even for your own
+personal use, without also meeting the above eight conditions for
+distributing the modified file. While you might intend that such
+modified files will never be distributed, often this will happen by
+accident -- you may forget that you have modified the file; or it may
+not occur to you when allowing others to access the modified file
+that you are thus distributing it and violating the conditions of
+this license. It is usually in your best interest to keep your copy
+of The Program identical with the public one. Many programs provide
+ways to control the behavior of that program without altering its
+licensed files.
+
+
+Additional Conditions on Individual Files of The Program
+--------------------------------------------------------
+
+An individual file of The Program may bear additional conditions that
+supplement and/or supersede the conditions in this license if, and only
+if, such additional conditions exclusively concern modification of the
+file or distribution of a modified version of the file. The conditions
+on individual files of The Program therefore may differ only with
+respect to the kind and extent of modification of those files that
+is allowed, and with respect to the distribution of modified versions
+of those files.
+
+
+Additional Conditions on LaTeX Software Files
+---------------------------------------------
+
+If a file of The Program is intended to be used with LaTeX (that is,
+if it is a LaTeX software file), then the following additional
+conditions, which supplement and/or supersede the conditions
+above, apply to the file according to its filename extension:
+
+ - You may not modify any file with filename extension `.ins' since
+ these are installation files containing the legal notices that are
+ placed in the files they generate.
+
+ - You may distribute modified versions of files with filename
+ extension `.fd' (LaTeX font definition files) under the standard
+ conditions of the LPPL as described above. You may also distribute
+ such modified LaTeX font definition files with their original names
+ provided that:
+ (1) the only changes to the original files either enable use of
+ available fonts or prevent attempts to access unavailable fonts;
+ (2) you also distribute the original, unmodified files (TeX input
+ paths can be used to control which set of LaTeX font definition
+ files is actually used by TeX).
+
+ - You may distribute modified versions of files with filename
+ extension `.cfg' (configuration files) with their original names.
+ The Program may (and usually will) specify the range of commands
+ that are allowed in a particular configuration file.
+
+Because of portability and exchangeability issues in LaTeX software,
+The LaTeX3 Project deprecates the distribution of modified versions of
+components of LaTeX or of generally available contributed code for them,
+but such distribution can meet the conditions of this license.
+
+
+NO WARRANTY
+===========
+
+There is no warranty for The Program. Except when otherwise stated in
+writing, The Copyright Holder provides The Program `as is', without
+warranty of any kind, either expressed or implied, including, but not
+limited to, the implied warranties of merchantability and fitness for
+a particular purpose. The entire risk as to the quality and performance
+of The Program is with you. Should The Program prove defective, you
+assume the cost of all necessary servicing, repair, or correction.
+
+In no event unless agreed to in writing will The Copyright Holder, or
+any author named in the files of The Program, or any other party who may
+distribute and/or modify The Program as permitted above, be liable to
+you for damages, including any general, special, incidental or
+consequential damages arising out of any use of The Program or out of
+inability to use The Program (including, but not limited to, loss of
+data, data being rendered inaccurate, or losses sustained by anyone as
+a result of any failure of The Program to operate with any other
+programs), even if The Copyright Holder or said author or said other
+party has been advised of the possibility of such damages.
+
+
+WHETHER AND HOW TO DISTRIBUTE PROGRAMS UNDER THIS LICENSE
+=========================================================
+
+This section contains important instructions, examples, and
+recommendations for authors who are considering distributing their
+programs under this license. These authors are addressed as `you' in
+this section.
+
+
+Choosing This License or Another License
+----------------------------------------
+
+If for any part of your program you want or need to use *distribution*
+conditions that differ from those in this license, then do not refer to
+this license anywhere in your program but instead distribute your
+program under a different license. You may use the text of this license
+as a model for your own license, but your license should not refer to
+the LPPL or otherwise give the impression that your program is
+distributed under the LPPL.
+
+The document `modguide.tex' in the base LaTeX distribution explains
+the motivation behind the conditions of this license. It explains,
+for example, why distributing LaTeX under the GNU General Public
+License (GPL) was considered inappropriate. Even if your program is
+unrelated to LaTeX, the discussion in `modguide.tex' may still be
+relevant, and authors intending to distribute their programs under any
+license are encouraged to read it.
+
+
+How to Use This License
+-----------------------
+
+To use this license, place in each of the files of your program both
+an explicit copyright notice including your name and the year and also
+a statement that the distribution and/or modification of the file is
+constrained by the conditions in this license.
+
+Here is an example of such a notice and statement:
+
+ %% pig.dtx
+ %% Copyright 2001 M. Y. Name
+ %
+ % This program may be distributed and/or modified under the
+ % conditions of the LaTeX Project Public License, either version 1.2
+ % of this license or (at your option) any later version.
+ % The latest version of this license is in
+ % http://www.latex-project.org/lppl.txt
+ % and version 1.2 or later is part of all distributions of LaTeX
+ % version 1999/12/01 or later.
+ %
+ % This program consists of the files pig.dtx and pig.ins
+
+Given such a notice and statement in a file, the conditions given in
+this license document would apply, with `The Program' referring to the
+two files `pig.dtx' and `pig.ins', and `The Copyright Holder' referring
+to the person `M. Y. Name'.
+
+
+Important Recommendations
+-------------------------
+
+ Defining What Constitutes The Program
+
+ The LPPL requires that distributions of The Program contain all the
+ files of The Program. It is therefore important that you provide a
+ way for the licensee to determine which files constitute The Program.
+ This could, for example, be achieved by explicitly listing all the
+ files of The Program near the copyright notice of each file or by
+ using a line like
+
+ % This program consists of all files listed in manifest.txt.
+
+ in that place. In the absence of an unequivocal list it might be
+ impossible for the licensee to determine what is considered by you
+ to comprise The Program.
+
+ Noting Exceptional Files
+
+ If The Program contains any files bearing additional conditions on
+ modification, or on distribution of modified versions, of those
+ files (other than those listed in `Additional Conditions on LaTeX
+ Software Files'), then it is recommended that The Program contain a
+ prominent file that defines the exceptional conditions, and either
+ lists the exceptional files or defines one or more categories of
+ exceptional files.
+
+ Files containing the text of a license (such as this file) are
+ often examples of files bearing more restrictive conditions on
+ modification. LaTeX configuration files (with filename extension
+ `.cfg') are examples of files bearing less restrictive conditions
+ on the distribution of a modified version of the file. The
+ additional conditions on LaTeX software given above are examples
+ of declaring a category of files bearing exceptional additional
+ conditions.
+
+
+
diff --git a/Master/texmf-dist/doc/latex/pbsheet/README b/Master/texmf-dist/doc/latex/pbsheet/README
new file mode 100644
index 00000000000..f3a61f3b003
--- /dev/null
+++ b/Master/texmf-dist/doc/latex/pbsheet/README
@@ -0,0 +1,61 @@
+TITLE
+ pbsheet LaTeX2e class.
+
+VERSION AND RELEASE DATE
+ v0.1, 2004-02-14.
+
+DESCRIPTION
+ pbsheet is a LaTeX2e document class dedicated to the formatting of teachers
+ problems sheets containing Mathematics, programs, and graphics.
+ Very simple to use, for daily usage.
+
+COPYRIGHT AND LICENSE
+ Copyright (C) Djalil CHAFAI, 2003, 2004. All files may be distributed and/or
+ modified under the conditions of the LaTeX Project Public License (LPPL),
+ either version 1.2 of this license or (at your option) any later version. The
+ latest version of this license is in http://www.latex-project.org/lppl.txt
+ and version 1.2 or later is part of all distributions of LaTeX version
+ 1999/12/01 or later. See the ./LPPL for a local copy of LPPL.
+
+FEEDBACK
+ http://www.lsp.ups-tlse.fr/Chafai/
+ E-mail: djalil DOT chafai AT laposte DOT net
+
+COMPILED AND TESTED WITH
+ teTeX 2.0.2, Debian/GNU Linux "testing" distribution.
+
+HOW TO BUILD
+ latex pbsheet.ins % generates the class file pbsheet.cls from pbsheet.dtx
+ latex pbsheet.dtx % generates the documentation pbsheet.dvi
+
+EXAMPLE OF USAGE
+ cd xpl-fr/
+ make ps pdf clean
+
+FILE LIST
+ pbsheet.cls pbsheet class (LaTeX2e).
+ pbsheet.ins pbsheet class installation file. LaTeX2e it to create the .cls
+ pbsheet.dtx pbsheet class commented code to generate the documentation.
+ pbsheet.dvi pbsheet class documentation in DVI format.
+ pbsheet.ps pbsheet class documentation in Postscript format.
+ pbsheet.pdf pbsheet class documentation in PDF format.
+ LPPL a copy of the LaTeX Project Public License.
+ README this file itself!
+ xpl/ dedicated directory to an example of pbsheet usage.
+ xpl/GNUmakefile GNU makefile for easy compilation of pbsheet example.
+ xpl/xpl-fr.tex source file of pbsheet example (in French).
+ xpl/xpl-fr.dvi compiled version of pbsheet example, in DVI format.
+ xpl/xpl-fr.ps compiled version of pbsheet example, in Postscript format.
+ xpl/xpl-fr.pdf compiled version of pbsheet example, in PDF format.
+ xpl/xpl-fr.bib BibTeX file for pbsheet example.
+ xpl/pgm/ Matlab code directory.
+ xpl/pgm/rdiscr.m some Matlab program.
+ xpl/pgm/rint.m Idem.
+ xpl/pgm/simbin.m Idem.
+ xpl/pgm/probadis.m Idem.
+ xpl/img/ EPS and PDF images directory.
+ xpl/img/simbin.eps some EPS graphic.
+ xpl/img/simbin.pdf the PDF version of the latter.
+
+EOF.
+
diff --git a/Master/texmf-dist/doc/latex/pbsheet/pbsheet.pdf b/Master/texmf-dist/doc/latex/pbsheet/pbsheet.pdf
new file mode 100644
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+% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
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+%!PS-AdobeFont-1.1: CMTT10 1.00B
+%%CreationDate: 1992 Apr 26 10:42:42
+% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
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+%%CreationDate: 1991 Aug 20 16:34:54
+% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
+11 dict begin
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+%%CreationDate: 1991 Aug 18 17:46:49
+% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
+11 dict begin
+/FontInfo 7 dict dup begin
+/version (1.0) readonly def
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+% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
+11 dict begin
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diff --git a/Master/texmf-dist/doc/latex/pbsheet/xpl/GNUmakefile b/Master/texmf-dist/doc/latex/pbsheet/xpl/GNUmakefile
new file mode 100644
index 00000000000..035b81b336c
--- /dev/null
+++ b/Master/texmf-dist/doc/latex/pbsheet/xpl/GNUmakefile
@@ -0,0 +1,85 @@
+# GNUmakefile, © 2003, 2004, Djalil CHAFAI.
+
+# Please adjust the following variables to your environment.
+
+BIBTEX=bibtex
+DVIPS=dvips -D 600 -t a4
+LATEX=latex #--src-specials
+PDFLATEX=pdflatex
+RM=rm
+THUMBPDF=thumbpdf
+
+# Normally, what follows does not need any modification.
+
+NOM=xpl-fr
+NOML=""
+MAKEFILENAME=GNUmakefile
+OUTPUTS=dvi ps pdf
+INTERMED=log out aux toc ind bbl blg lol lof lot ilg idx inc rel brf tpt
+FIGSDIR=img
+CODESDIR=pgm
+TEXINPUTS:=.:./$(FIGSDIR)//:./$(CODESDIR)//:$(TEXINPUTS)
+export TEXINPUTS
+
+# Static sources related variables.
+
+TEX= $(NOM).bib $(NOM).tex
+MISC1= $(shell kpsewhich amsalpha.bst)
+MISC2= $(wildcard $(FIGSDIR)/* $(CODESDIR)/*) $(MAKEFILENAME)
+SRC= $(MISC1) $(MISC2) $(TEX)
+
+# Dependencies.
+
+DEP_PS=$(MAKEFILENAME) $(MISC1) $(TEX)
+DEP_PDF=$(MAKEFILENAME) $(MISC1) $(TEX)
+DEP_ARCH=$(SRC) $(NOM).ps $(NOM).pdf
+
+
+# Special variables.
+
+.PHONY= $(OUTPUTS) help clean cleanall
+.PHONY: $(.PHONY)
+.SUFFIXES:
+.INTERMEDIATE: $(INTERMDED:%=$(NOM).%)
+
+# Phony rules.
+
+help:
+ @echo
+ @echo " Rules to compile $(NOM).tex : $(.PHONY)."
+ @echo " For example «make ps» will make the PS file for you!"
+ @echo
+
+dvi: clean $(NOM).dvi
+ps: $(NOM).ps
+pdf: clean $(NOM).pdf
+
+clean:
+ @$(RM) -f $(INTERMED:%=$(NOM).%) thb*.png *~ *.aux *.inc
+ @$(RM) -f $(CODESDIR)/*~ $(FIGSDIR)/*~
+ @$(RM) -rf auto
+
+cleanall: clean
+ @for f in $(OUTPUTS); do $(RM) -f $(NOM).$$f; done
+
+# Rules based on target files.
+
+$(NOM).ps: $(NOM).dvi
+ @$(DVIPS) $(NOM).dvi -o $(NOM).ps
+
+$(NOM).dvi: $(DEP_PS)
+ @$(LATEX) $(NOM)
+ @$(BIBTEX) $(NOM)
+ @$(LATEX) $(NOM)
+ @$(LATEX) $(NOM)
+ @$(LATEX) $(NOM)
+
+$(NOM).pdf: $(DEP_PDF)
+ @$(PDFLATEX) $(NOM)
+ @$(BIBTEX) $(NOM)
+ @$(PDFLATEX) $(NOM)
+ @$(PDFLATEX) $(NOM)
+ @$(THUMBPDF) $(NOM).pdf
+ @$(PDFLATEX) $(NOM)
+
+# End Of File.
diff --git a/Master/texmf-dist/doc/latex/pbsheet/xpl/img/simbin.eps b/Master/texmf-dist/doc/latex/pbsheet/xpl/img/simbin.eps
new file mode 100644
index 00000000000..6403e0671f9
--- /dev/null
+++ b/Master/texmf-dist/doc/latex/pbsheet/xpl/img/simbin.eps
@@ -0,0 +1,2459 @@
+%!PS-Adobe-2.0 EPSF-2.0
+%%Title: gauss.eps
+%%Creator: gnuplot 3.7 patchlevel 3
+%%CreationDate: Mon Dec 8 17:23:19 2003
+%%DocumentFonts: (atend)
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+%%BoundingBox: 0 44 300 255
+%%EndComments
+%%BeginProcSet: epsffit 1 0
+gsave
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+%%EndProcSet
+
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+ dup stringwidth pop -2 div vshift R show } def
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+ /hpt2 hpt 2 mul def /vpt2 vpt 2 mul def } def
+/DL { Color {setrgbcolor Solid {pop []} if 0 setdash }
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+showpage
+%%Trailer
+%%DocumentFonts: Helvetica
+grestore
diff --git a/Master/texmf-dist/doc/latex/pbsheet/xpl/img/simbin.pdf b/Master/texmf-dist/doc/latex/pbsheet/xpl/img/simbin.pdf
new file mode 100644
index 00000000000..f4f8166c75e
--- /dev/null
+++ b/Master/texmf-dist/doc/latex/pbsheet/xpl/img/simbin.pdf
Binary files differ
diff --git a/Master/texmf-dist/doc/latex/pbsheet/xpl/pbsheet.cls b/Master/texmf-dist/doc/latex/pbsheet/xpl/pbsheet.cls
new file mode 100644
index 00000000000..653c9b9c610
--- /dev/null
+++ b/Master/texmf-dist/doc/latex/pbsheet/xpl/pbsheet.cls
@@ -0,0 +1,551 @@
+%%
+%% This is file `pbsheet.cls',
+%% generated with the docstrip utility.
+%%
+%% The original source files were:
+%%
+%% pbsheet.dtx (with options: `class')
+%%
+%% This is a generated file.
+%%
+%% Copyright (C) 2003, 2004 Djalil CHAFAI
+%% djalil DOT chafai AT laposte DOT net
+%% http;//www.lsp.ups-tlse.fr/Chafai/pbsheet.html
+%%
+%% This file may be distributed and/or modified under the conditions of
+%% the LaTeX Project Public License, either version 1.2 of this license
+%% or (at your option) any later version. The latest version of this
+%% license is in:
+%%
+%% http://www.latex-project.org/lppl.txt
+%%
+%% and version 1.2 or later is part of all distributions of LaTeX version
+%% 1999/12/01 or later.
+%%
+\NeedsTeXFormat{LaTeX2e}[1999/12/01]
+\ProvidesClass{pbsheet}
+ [2004/02/14 v0.1 .dtx pbsheet file]
+\ClassInfo{pbsheet}{Copyright (c) Djalil CHAFAI, 2003, 2004.}
+\ClassInfo{pbsheet}{http://www.lsp.ups-tlse.fr/Chafai/}
+\ClassInfo{pbsheet}{chafai AT math DOT ups-tlse DOT fr}
+%%
+\LoadClassWithOptions{article} \ProcessOptions\relax
+%%
+\ifx\pdfoutput\undefined
+ \usepackage[latin1]{inputenc}
+ \usepackage[T1]{fontenc}
+ \usepackage{url}
+ \usepackage[dvips]{graphicx}
+ \newcommand{\phantomsection}{\null} %% provided by hyperref.
+\else
+ \pdfoutput=1\pdfcompresslevel=9\pdfadjustspacing=1
+ \usepackage[pdftex,bookmarks,a4paper,colorlinks]{hyperref}
+ \usepackage{aeguill}
+ \usepackage[pdftex]{graphicx}
+ \hypersetup{bookmarksnumbered,plainpages=false,hypertexnames=false}
+ \hypersetup{pagecolor=blue,linkcolor=blue,citecolor=blue,urlcolor=blue}
+ \hypersetup{pdfcreator=PDFLaTeX with pbsheet class}
+\fi
+\RequirePackage{amsmath,amsfonts,amssymb,amsthm,latexsym}
+\RequirePackage[a4paper,portrait]{geometry}
+\RequirePackage{rotating}
+\RequirePackage{moreverb}
+\RequirePackage[latin1]{inputenc}
+\RequirePackage{xspace}
+\RequirePackage[francais]{babel}
+\RequirePackage{color}
+\RequirePackage{listings}
+\ifx\pdfoutput\undefined
+\else %% listings/hyperref compatibility.
+ \makeatletter
+ \providecommand*{\toclevel@lstlisting}{0}
+ \makeatother
+\fi
+%%%%
+%%%% Macros et Environments
+%%%%
+%%
+\newcommand{\MFILE}[1]{
+ \begin{lstinputlisting}[language=Matlab]{#1.m}%
+ \label{code:#1}%
+ \end{lstinputlisting}
+}
+%%
+\newcommand{\SCEFILE}[1]{
+ \begin{lstinputlisting}[language=Scilab]{#1.sce}%
+ \label{code:#1}%
+ \end{lstinputlisting}
+}
+%%
+\newcommand{\SCIFILE}[1]{
+ \begin{lstinputlisting}[language=Scilab]{#1.sci}%
+ \label{code:#1}%
+ \end{lstinputlisting}
+}
+%%
+\newcommand{\FFIG}[5]{%% fname cm scale floatparams caption
+%% here, floatparams is in the set {vflt,rflt,lflt}, cf. floatflt doc.
+ \begin{floatingfigure}[#4]{#2}%
+ \begin{center}%
+ \includegraphics[scale=#3]{#1}%
+ \caption{#5}%
+ \label{fi:#1}%
+ \end{center}%
+ \end{floatingfigure}%
+}
+%%
+\newcommand{\FIG}[4]{%% fname scale floatparams caption
+ \begin{figure}[#3]%
+ \begin{center}%
+ \includegraphics[scale=#2]{#1}%
+ \caption{{#4}}%
+ \label{fi:#1}%
+ \end{center}%
+ \end{figure}
+}
+%%
+\makeatletter%
+\newcommand{\@TITRE}{Feuille de Travaux Pratiques}
+\newcommand{\@AUTEUR}{Anonyme}
+\newcommand{\@DATE}{\today}
+\newcommand{\@FORMATION}{Agr\'egation de math\'ematiques%
+ -- Oral de mod\'elisation stochastique}
+\newcommand{\@ANNEE}{Ann\'ee}
+\newcommand{\@ETABLISSEMENT}{\'Etablissement}
+\newcommand{\@WEB}{http://www.lsp.ups-tlse.fr/Chafai/agregteam.html}
+\newcommand{\@MEL}{anonyme@pas.net}
+\newcommand{\TITRE}[1]{%
+ \renewcommand{\@TITRE}{#1}}
+\newcommand{\AUTEUR}[1]{%
+ \renewcommand{\@AUTEUR}{#1}}
+\newcommand{\DATE}[1]{%
+ \renewcommand{\@DATE}{#1}}
+\newcommand{\FORMATION}[1]{%
+ \renewcommand{\@FORMATION}{#1}}
+\newcommand{\ANNEE}[1]{%
+ \renewcommand{\@ANNEE}{#1}}
+\newcommand{\ETABLISSEMENT}[1]{%
+ \renewcommand{\@ETABLISSEMENT}{#1}}
+\newcommand{\WEB}[1]{%
+ \renewcommand{\@WEB}{#1}}
+\newcommand{\MEL}[1]{%
+ \renewcommand{\@MEL}{#1}}
+\makeatother
+%%
+\makeatletter
+\newcommand{\PREMIEREPAGE}{%
+ \newpage\null%
+ \begin{center}%
+ \hrule height .2pt%
+ \medskip{\Large\bfseries\@TITRE\par}\medskip%
+ \hrule height .2pt%
+ \end{center}%
+ \bigskip%\vfil%
+}
+\makeatother
+%%
+\theoremstyle{plain}%
+\newtheorem{thm}{Theor\`eme}[section]%
+\newtheorem{cor}[thm]{Corollaire}%
+\newtheorem{prop}[thm]{Proposition}%
+\newtheorem{lem}[thm]{Lemme}%
+\theoremstyle{definition}%
+\newtheorem{defi}[thm]{D\'efinition}%
+\newtheorem{xpl}[thm]{Exemple}%
+\newtheorem{exo}[thm]{Exercice}%
+\newtheorem{hyp}[thm]{Hypoth\`ese}%
+\newtheorem{eur}[thm]{Heuristique}%
+\newtheorem{pro}[thm]{Probl\`eme}%
+\theoremstyle{remark}%
+\newtheorem{rem}[thm]{Remarque}%
+%%%%
+%%%% Commands to be executed before \begin{document}
+%%%%
+%%
+\geometry{left=2.5cm,right=2.5cm}
+%%
+\lstset{extendedchars=true,%
+ basicstyle=\small,%
+ commentstyle=\ttfamily\color[rgb]{0,0,0.5},%
+ stringstyle=\color[rgb]{0,0.5,0},%
+ frame=tblr,frameround=tttt,%
+ %%labelstyle=\tiny,labelstep=1,labelsep=10pt
+}
+%%
+\makeatletter
+\renewcommand{\@evenfoot}
+{\tiny\normalfont
+ \@DATE. Copyright ^^a9 \@AUTEUR\ \@MEL. GNU FDL Copyleft.
+%% \url{http://www.gnu.org/copyleft/fdl.html}.
+ \hfil \upshape Page n^^b0{\thepage}.}
+\renewcommand{\@evenhead}
+{\tiny\scshape \@ETABLISSEMENT\ -- \@FORMATION\ --
+ \normalfont\bfseries\@ANNEE.
+ \normalfont\hfil \upshape Page n^^b0{\thepage}.}
+\renewcommand{\@oddfoot}{\@evenfoot}
+\renewcommand{\@oddhead}{\@evenhead}
+\makeatother
+%% smaller sections titles
+\makeatletter
+\renewcommand{\section}{\@startsection%
+ {section}% % name
+ {1}% % level
+ {0em}% % indent
+ {\baselineskip}% % beforeskip
+ {0.5\baselineskip}% % afterskip
+ {\normalfont\large\bfseries}}% % style
+\renewcommand{\subsection}{\@startsection%
+ {subsection}% % name
+ {2}% % level
+ {0em}% % indent
+ {\baselineskip}% % beforeskip
+ {0.25\baselineskip}% % afterskip
+ {\normalfont\bfseries}% % style
+}
+\makeatother
+%%
+%% Macros
+%%
+\newcommand{\DOIFPDF}[2]{\ifx\pdfoutput\undefined #2\else#1\fi}
+%% For nice typesetting of the actual engine name.
+\newcommand{\EngineName}{\DOIFPDF{\texttt{pdf}\LaTeX}{\LaTeXe}}
+%% For short rough notes and warnings.
+\newcommand{\NB}[1]{{\large\textbf{*** #1 ***}}}
+%% To force maths mode.
+\newcommand{\EM}{\ensuremath}
+%%% Limits
+\newcommand{\limLeb}[2]
+ {\underset{#1\to+\infty}{\overset{\bL^{#2}}{\longrightarrow}}}
+\newcommand{\limE}[1]
+ {\underset{#1\to+\infty}{\overset{\text{^^e9tr.}}{\longrightarrow}}}
+\newcommand{\limW}[1]
+ {\underset{#1\to+\infty}{\overset{\text{weak}}{\longrightarrow}}}
+\newcommand{\limP}[1]
+ {\underset{#1\to+\infty}{\overset{\dP}{\longrightarrow}}}
+\newcommand{\limL}[1]
+ {\underset{#1\to+\infty}{\overset{\cL}{\longrightarrow}}}
+\newcommand{\limn}[1]
+ {\underset{#1\to+\infty}{\longrightarrow}}
+\newcommand{\mylim}[2]
+ {\underset{#1\to#2}{\longrightarrow}}
+\newcommand{\limPS}[1]
+ {\underset{#1\to+\infty}{\overset{\text{p.s.}}{\longrightarrow}}}
+\newcommand{\limAS}[1]
+ {\underset{#1\to+\infty}{\overset{\text{a.s.}}{\longrightarrow}}}
+%% Time
+\makeatletter
+\providecommand{\timenow}{\@tempcnta\time%
+\@tempcntb\@tempcnta%
+\divide\@tempcntb60%
+\ifnum10>\@tempcntb0\fi\number\@tempcntb%
+\multiply\@tempcntb60%
+\advance\@tempcnta-\@tempcntb%
+:\ifnum10>\@tempcnta0\fi\number\@tempcnta}
+\makeatother
+%% Mathmode double capital letters.
+\newcommand{\dA}{\EM{\mathbb{A}}}
+\newcommand{\dB}{\EM{\mathbb{B}}}
+\newcommand{\dC}{\EM{\mathbb{C}}}
+\newcommand{\dD}{\EM{\mathbb{D}}}
+\newcommand{\dE}{\EM{\mathbb{E}}}
+\newcommand{\dF}{\EM{\mathbb{F}}}
+\newcommand{\dG}{\EM{\mathbb{G}}}
+\newcommand{\dH}{\EM{\mathbb{H}}}
+\newcommand{\dI}{\EM{\mathbb{I}}}
+\newcommand{\dJ}{\EM{\mathbb{J}}}
+\newcommand{\dK}{\EM{\mathbb{K}}}
+\newcommand{\dL}{\EM{\mathbb{L}}}
+\newcommand{\dM}{\EM{\mathbb{M}}}
+\newcommand{\dN}{\EM{\mathbb{N}}}
+\newcommand{\dO}{\EM{\mathbb{O}}}
+\newcommand{\dP}{\EM{\mathbb{P}}}
+\newcommand{\dQ}{\EM{\mathbb{Q}}}
+\newcommand{\dR}{\EM{\mathbb{R}}}
+\newcommand{\dS}{\EM{\mathbb{S}}}
+\newcommand{\dT}{\EM{\mathbb{T}}}
+\newcommand{\dU}{\EM{\mathbb{U}}}
+\newcommand{\dV}{\EM{\mathbb{V}}}
+\newcommand{\dW}{\EM{\mathbb{W}}}
+\newcommand{\dX}{\EM{\mathbb{X}}}
+\newcommand{\dY}{\EM{\mathbb{Y}}}
+\newcommand{\dZ}{\EM{\mathbb{Z}}}
+%% Mathmode Roman capital letters.
+\newcommand{\rA}{\EM{\mathrm{A}}}
+\newcommand{\rB}{\EM{\mathrm{B}}}
+\newcommand{\rC}{\EM{\mathrm{C}}}
+\newcommand{\rD}{\EM{\mathrm{D}}}
+\newcommand{\rE}{\EM{\mathrm{E}}}
+\newcommand{\rF}{\EM{\mathrm{F}}}
+\newcommand{\rG}{\EM{\mathrm{G}}}
+\newcommand{\rH}{\EM{\mathrm{H}}}
+\newcommand{\rI}{\EM{\mathrm{I}}}
+\newcommand{\rJ}{\EM{\mathrm{J}}}
+\newcommand{\rK}{\EM{\mathrm{K}}}
+\newcommand{\rL}{\EM{\mathrm{L}}}
+\newcommand{\rM}{\EM{\mathrm{M}}}
+\newcommand{\rN}{\EM{\mathrm{N}}}
+\newcommand{\rO}{\EM{\mathrm{O}}}
+\newcommand{\rP}{\EM{\mathrm{P}}}
+\newcommand{\rQ}{\EM{\mathrm{Q}}}
+\newcommand{\rR}{\EM{\mathrm{R}}}
+\newcommand{\rS}{\EM{\mathrm{S}}}
+\newcommand{\rT}{\EM{\mathrm{T}}}
+\newcommand{\rU}{\EM{\mathrm{U}}}
+\newcommand{\rV}{\EM{\mathrm{V}}}
+\newcommand{\rW}{\EM{\mathrm{W}}}
+\newcommand{\rX}{\EM{\mathrm{X}}}
+\newcommand{\rY}{\EM{\mathrm{Y}}}
+\newcommand{\rZ}{\EM{\mathrm{Z}}}
+%% Mathmode calligraphic capital letters.
+\newcommand{\cA}{\EM{\mathcal{A}}}
+\newcommand{\cB}{\EM{\mathcal{B}}}
+\newcommand{\cC}{\EM{\mathcal{C}}}
+\newcommand{\cD}{\EM{\mathcal{D}}}
+\newcommand{\cE}{\EM{\mathcal{E}}}
+\newcommand{\cF}{\EM{\mathcal{F}}}
+\newcommand{\cG}{\EM{\mathcal{G}}}
+\newcommand{\cH}{\EM{\mathcal{H}}}
+\newcommand{\cI}{\EM{\mathcal{I}}}
+\newcommand{\cJ}{\EM{\mathcal{J}}}
+\newcommand{\cK}{\EM{\mathcal{K}}}
+\newcommand{\cL}{\EM{\mathcal{L}}}
+\newcommand{\cM}{\EM{\mathcal{M}}}
+\newcommand{\cN}{\EM{\mathcal{N}}}
+\newcommand{\cO}{\EM{\mathcal{O}}}
+\newcommand{\cP}{\EM{\mathcal{P}}}
+\newcommand{\cQ}{\EM{\mathcal{Q}}}
+\newcommand{\cR}{\EM{\mathcal{R}}}
+\newcommand{\cS}{\EM{\mathcal{S}}}
+\newcommand{\cT}{\EM{\mathcal{T}}}
+\newcommand{\cU}{\EM{\mathcal{U}}}
+\newcommand{\cV}{\EM{\mathcal{V}}}
+\newcommand{\cW}{\EM{\mathcal{W}}}
+\newcommand{\cX}{\EM{\mathcal{X}}}
+\newcommand{\cY}{\EM{\mathcal{Y}}}
+\newcommand{\cZ}{\EM{\mathcal{Z}}}
+%% Mathmode bold capital letters.
+\newcommand{\bA}{\EM{\mathbf{A}}}
+\newcommand{\bB}{\EM{\mathbf{B}}}
+\newcommand{\bC}{\EM{\mathbf{C}}}
+\newcommand{\bD}{\EM{\mathbf{D}}}
+\newcommand{\bE}{\EM{\mathbf{E}}}
+\newcommand{\bF}{\EM{\mathbf{F}}}
+\newcommand{\bG}{\EM{\mathbf{G}}}
+\newcommand{\bH}{\EM{\mathbf{H}}}
+\newcommand{\bI}{\EM{\mathbf{I}}}
+\newcommand{\bJ}{\EM{\mathbf{J}}}
+\newcommand{\bK}{\EM{\mathbf{K}}}
+\newcommand{\bL}{\EM{\mathbf{L}}}
+\newcommand{\bM}{\EM{\mathbf{M}}}
+\newcommand{\bN}{\EM{\mathbf{N}}}
+\newcommand{\bO}{\EM{\mathbf{O}}}
+\newcommand{\bP}{\EM{\mathbf{P}}}
+\newcommand{\bQ}{\EM{\mathbf{Q}}}
+\newcommand{\bR}{\EM{\mathbf{R}}}
+\newcommand{\bS}{\EM{\mathbf{S}}}
+\newcommand{\bT}{\EM{\mathbf{T}}}
+\newcommand{\bU}{\EM{\mathbf{U}}}
+\newcommand{\bV}{\EM{\mathbf{V}}}
+\newcommand{\bW}{\EM{\mathbf{W}}}
+\newcommand{\bX}{\EM{\mathbf{X}}}
+\newcommand{\bY}{\EM{\mathbf{Y}}}
+\newcommand{\bZ}{\EM{\mathbf{Z}}}
+%% Useful shortcuts to some Greek letters and symbols.
+\newcommand{\al}{\alpha}
+\newcommand{\be}{\beta}
+\newcommand{\De}{\Delta}
+\newcommand{\de}{\delta}
+\newcommand{\ga}{\gamma}
+\newcommand{\Ga}{\Gamma}
+\newcommand{\g}{\gamma}
+\newcommand{\gn}{\g_n}
+\newcommand{\gt}[1]{\g^{\otimes #1}}
+\newcommand{\la}{\lambda}
+\newcommand{\La}{\Lambda}
+\newcommand{\lan}{\la_n}
+\newcommand{\na}{\nabla}
+\newcommand{\Om}{\Omega}
+\newcommand{\om}{\omega}
+\newcommand{\ph}{\Phi}
+\newcommand{\Si}{\Sigma}
+\newcommand{\si}{\sigma}
+\newcommand{\Te}{\Theta}
+\newcommand{\te}{\theta}
+\newcommand{\ta}{\tau}
+\newcommand{\Ups}{\Upsilon}
+\newcommand{\veps}{\varepsilon}
+\newcommand{\vphi}{\varphi}
+\newcommand{\bul}{\EM{\bullet}}
+%% Functional prototype with dimensioning.
+\newcommand{\p}[4]{{#3}\!\left#1{#4}\right#2}
+%% Norms and related.
+\newcommand{\ABS}[1]{\EM{{\left| #1 \right|}}} % |1|
+\newcommand{\BRA}[1]{\EM{{\left\{#1\right\}}}} % {1}
+\newcommand{\DP}[1]{\EM{{\left<#1\right>}}} % <1>
+\newcommand{\NRM}[1]{\EM{{\left\| #1\right\|}}} % ||1||
+\newcommand{\NI}[1]{\EM{{\left\| #1\right\|}_\infty}} % infinite norm.
+\newcommand{\OSC}[1]{\EM{{\p(){\mathrm{osc}}{#1}}}} % oscillation.
+\newcommand{\PAR}[1]{\EM{{\left(#1\right)}}} % (1)
+\newcommand{\BPAR}[1]{\EM{{\biggl(#1\biggr)}}} % (1)
+\newcommand{\BABS}[1]{\EM{{\biggl|#1\biggr|}}} % (1)
+\newcommand{\pd}{\EM{\partial}} % derivee partielle
+\newcommand{\PD}[2]{\EM{{\frac{\partial #1}{\partial #2}}}}%part. deriv.
+\newcommand{\SBRA}[1]{\EM{{\left[#1\right]}}} % [1]
+\newcommand{\VT}[1]{\EM{{\|#1\|}_{\text{\scriptsize VT}}}} % tot. var.
+\newcommand{\LIP}[1]{\EM{\|#1\|_{\mathrm{Lip}}}} % Lipschitz norm.
+\newcommand{\WH}[1]{\widehat{#1}}
+%% Fonctionals and functions.
+\newcommand{\sentf}{\bH}
+\newcommand{\sent}[1]{\p(){\sentf}{#1}}
+\newcommand{\bentf}[1]{\bH_{#1}}
+\newcommand{\bent}[2]{\p(){\bentf{#1}}{#2}}
+\newcommand{\eentf}{\bN}
+\newcommand{\eent}[1]{\p(){\eentf}{#1}}
+\newcommand{\entf}[1]{\mathbf{Ent}_{#1}}
+\newcommand{\ent}[2]{\p(){\entf{#1}}{#2}}
+\newcommand{\ientf}[1]{\bH^{#1}}
+\newcommand{\ient}[2]{\p(){\ientf{#1}}{#2}}
+\newcommand{\rentf}{\mathbf{Ent}}
+\newcommand{\rent}[2]{\p(){\rentf}{#1\,\vert\,#2}}
+\newcommand{\entr}{\mathbf{Ent}_r}
+\newcommand{\enef}[1]{\boldsymbol{\mathcal{E}}_{#1}}
+\newcommand{\ene}[2]{\p(){\enef{#1}}{#2}}
+\newcommand{\imutf}{\bI}
+\newcommand{\imut}[1]{\p(){\imutf}{#1}}
+\newcommand{\fcrf}{\dI}
+\newcommand{\fcr}[1]{\p(){\fcrf}{#1}}
+\newcommand{\fishf}{\bJ}
+\newcommand{\fish}[1]{\p(){\fishf}{#1}}
+\newcommand{\fishmf}{\dJ}
+\newcommand{\fishm}[1]{\p(){\fishmf}{#1}}
+\newcommand{\moyf}[1]{\bE_{#1}}
+\newcommand{\moy}[2]{\p(){\moyf{#1}}{#2}}
+\newcommand{\econd}[2]{\p(){\moyf{}}{#1\,\vert\,#2}}
+\newcommand{\bmoy}[2]{\moyf{#1}\!\biggl(#2\biggr)}
+\newcommand{\corrf}[1]{\mathbf{Cor}_{#1}}
+\newcommand{\corr}[3]{\p(){\corrf{#1}}{#2,#3}}
+\newcommand{\covf}[1]{\mathbf{Cov}_{#1}}
+\newcommand{\cov}[3]{\p(){\covf{#1}}{#2,#3}}
+\newcommand{\bcov}[3]{\covf{#1}\!\biggl(#2,#3\biggr)}
+\newcommand{\suppf}{\mathrm{supp}}
+\newcommand{\supp}[1]{\suppf\PAR{#1}}
+\newcommand{\DIMF}{\mathrm{dim}}
+\newcommand{\DIM}[1]{\DIMF\PAR{#1}}
+\newcommand{\RANGEF}{\mathrm{range}}
+\newcommand{\RANGE}[1]{\RANGEF\PAR{#1}}
+\newcommand{\varf}[1]{\mathbf{Var}_{#1}}
+\newcommand{\var}[2]{\p(){\varf{#1}}{#2}}
+\newcommand{\bvar}[2]{\varf{#1}\!\biggl(#2\biggr)}
+\newcommand{\Kf}{\bK}
+\newcommand{\K}[1]{\p(){\Kf}{#1}}
+\newcommand{\vrs}[1]{\mathbf{L}_{#1}}
+\newcommand{\lik}[1]{\vrs{#1}}
+%% Sets, spaces, and functional spaces.
+\newcommand{\C}[1]{\p(){\cC}{#1}}
+\newcommand{\Cb}[1]{\p(){\cC_b}{#1}}
+\newcommand{\Cc}[1]{\p(){\cC_c}{#1}}
+\newcommand{\Cn}[2]{\p(){\cC^{#1}}{#2}}
+\newcommand{\Ci}[1]{\Cn{\infty}{#1}}
+\newcommand{\Cic}[1]{\p(){\cC_c^\infty}{#1}}
+\newcommand{\Cnc}[2]{\p(){\cC_c^{#1}}{#2}}
+\newcommand{\Cnb}[2]{\p(){\cC_b^{#1}}{#2}}
+\newcommand{\Cib}[1]{\p(){\cC_b^\infty}{#1}}
+\newcommand{\leb}[2]{\p(){\bL^{#1}}{#2}}
+\newcommand{\lebb}[1]{\bL^{#1}}
+%% Determinant, trace, ...
+\newcommand{\Tr}{\mathrm{Tr\,}}
+\newcommand{\Det}[1]{\mathrm{Det}\,}
+\newcommand{\TR}[1]{\p(){\mathrm{Tr}}{#1}}
+\newcommand{\DIAG}[1]{\p(){\mathrm{Diag}}{#1}}
+\newcommand{\DET}[1]{\p(){\mathrm{Det}}{#1}}
+\newcommand{\SIG}[1]{\p(){\mathrm{Sign}}{#1}}
+\newcommand{\KER}[1]{\p(){\mathrm{Ker}}{#1}}
+\newcommand{\RG}[1]{\p(){\mathrm{Range}}{#1}}
+\newcommand{\DIAM}[1]{\p(){\mathrm{Diam}}{#1}}
+\newcommand{\ID}{\mathbf{Id}}
+\newcommand{\Id}{\mathrm{Id}}
+\newcommand{\Mo}{\mathbf{1}}
+\newcommand{\Vo}{\mathrm{1}}
+%%% Semi-groups, generators, carre-du-champ, ...
+\newcommand{\CD}{CD(\rho ,\infty)}
+\newcommand{\GA}{\boldsymbol{\Gamma}}
+\newcommand{\GD}{\GA_{\!\!{\mathbf 2}}}
+\newcommand{\GI}{\bL}
+\newcommand{\GR}{\nabla}
+\newcommand{\GIV}{\EM{\overrightarrow{\GI}}}
+\newcommand{\GIB}{\EM{\overline{\GI}}}
+\newcommand{\LA}{\boldsymbol{\Delta}}
+\newcommand{\ROT}{\mathbf{rot}\,}
+\newcommand{\DIV}{\mathbf{div}\,}
+\newcommand{\PT}[1][t]{\mathbf{P}_{\!#1}}
+\newcommand{\SGf}[1]{{\mathbf P}_{#1}}
+\newcommand{\SG}[2]{\p(){\SGf{\!#1}}{#2}}
+\newcommand{\SGQf}[1]{{\mathbf Q}_{#1}}
+\newcommand{\SGQ}[2]{\p(){\SGQf{#1}}{#2}}
+\newcommand{\isopf}{\mathbf{I}}
+\newcommand{\isop}[1]{\p(){\isopf}{#1}}
+\newcommand{\disop}[1]{\p(){\isopf'}{#1}}
+\newcommand{\ddisop}[1]{\p(){\isopf''}{#1}}
+\newcommand{\HESS}[1]{\GR^2\!{#1}}
+\newcommand{\Hess}[1]{{\p(){\mathrm{Hess}}{#1}}}
+\newcommand{\HAM}{\bH}
+\newcommand{\POT}{\bV}
+\newcommand{\PF}{\bZ}
+\newcommand{\DOM}{\EM{\cD_2(\GI)}}
+\newcommand{\laV}{\EM{\overrightarrow{\la}}}
+\newcommand{\DOML}{\EM{\cD_2\PAR{\GI}}}
+\newcommand{\DOMB}{\EM{\cD_2(\GIB)}}
+\newcommand{\DOMV}{\EM{\cD_2(\GIV)}}
+\newcommand{\GAV}{\EM{\overrightarrow{\GA}}}
+\newcommand{\D}{\mathbf{D}}
+%% Topology.
+\newcommand{\inter}[1]{{\overset{\circ}{#1}}} % interior
+\newcommand{\adher}[1]{{\overline{#1}}} % adherence
+\newcommand{\ADH}[1]{\mathbf{adh}(#1)}
+\newcommand{\INT}[1]{\mathbf{int}(#1)}
+%% Miscellany.
+\newcommand{\DOTIMES}{\otimes\cdots\otimes}
+\newcommand{\DOPLUS}{\oplus\cdots\oplus}
+\newcommand{\CARD}{\mathrm{card}}
+\newcommand{\SSK}[1]{\substack{#1}}
+\renewcommand{\leq}{\leqslant}
+\renewcommand{\geq}{\geqslant}
+\newcommand{\bs}{\EM{\backslash}}
+\newcommand{\Inf}{\boldsymbol{\inf}}
+\newcommand{\Sup}{\boldsymbol{\sup}}
+\newcommand{\ds}[1]{\EM{\displaystyle{#1}}}
+\newcommand{\eg}{\overset{\Delta}{=}}
+\newcommand{\fdefeq}{\overset{\text{d^^e9f.}}{=}}
+\newcommand{\edefeq}{\overset{\text{def.}}{=}}
+\newcommand{\defeq}{:=}
+\newcommand{\equ}{\; \Leftrightarrow \;}
+\newcommand{\ex}{\exists \,}
+\newcommand{\imp}{\Rightarrow \;}
+\newcommand{\ssi}{{\it ssi}}
+\newcommand{\tout}{\forall \,}
+\newcommand{\tq}{\,|\,}
+\newcommand{\st}{\,|\,}
+\newcommand{\DSFRAC}[2]{\EM{\frac{\ds{#1}}{\ds{#2}}}}
+\newcommand{\SR}[2]{\EM{\strackrel{#1}{#2}}}
+\def\Ieme{\up{\lowercase{i^^e8me}}\xspace}
+%% Vectors and matrices.
+\newcommand{\VECTOR}[1]{\PAR{\begin{array}{c} #1 \end{array}}}
+\newcommand{\BIMATRIX}[1]{\PAR{\begin{array}{cc} #1 \end{array}}}
+\newcommand{\Vector}[2]{\PAR{\begin{array}{#1} #2 \end{array}}}
+\newcommand{\Bimatrix}[2]{\PAR{\begin{array}{#1} #2 \end{array}}}
+%%%%
+%%%% Commands to be executed just after \begin{document}
+%%%%
+\AtBeginDocument{%
+ \selectlanguage{francais}%
+ \graphicspath{{images/}{img/}{Images}{Img}{ps}{eps}{PS}{EPS}%
+ {postscript}{postscripts}{pdf}{PDF}}%
+ \PREMIEREPAGE%
+}
+%%%%
+%%%% Commands to be executed just before \end{document}
+%%%%
+\AtEndDocument{\vfill}
+\endinput
+%%
+%% End of file `pbsheet.cls'.
diff --git a/Master/texmf-dist/doc/latex/pbsheet/xpl/pgm/probadis.m b/Master/texmf-dist/doc/latex/pbsheet/xpl/pgm/probadis.m
new file mode 100644
index 00000000000..7f472ad4045
--- /dev/null
+++ b/Master/texmf-dist/doc/latex/pbsheet/xpl/pgm/probadis.m
@@ -0,0 +1,65 @@
+function res = probadis(x,p)
+%res = PROBADIS(x,p)
+% Input x vector of real numbers (support points in IR)
+% p vector of probability weights associated to x
+% i.e. non-negative real numbers such that sum(p) == 1
+% Output res random number chosen from the finite discrete
+% distribution on x(1),...,x(n) with probability weights
+% p(1),...,p(n) where n == length(x) == length(p)
+%
+% Renvoie UNE réalisation de la loi discrète à support fini sur IR dont les
+% points de support sont les composantes du vecteur x, et les poids sont les
+% composantes du vecteur p. Donc x(i) a une probabilité p(i) d'être renvoyé.
+%
+% La méthode consiste à écrire l'intervalle [0,1] comme une réunion disjointe
+% d'intervalles de longueurs p(1),..., p(n) puis à regarder au quel appartient
+% la réalisation d'une loi uniforme obtenue par un appel à rand. Les valeurs
+% renvoyées par des appels successifs sont donc pseudo-indépendantes.
+% Pour des raisons d'efficacité, les conditions nécessaires suivantes ne sont
+% pas contrôlées par cette fonction :
+% - le nombre de paramètres passés est exactement 2
+% - les deux paramètres x et p sont bien des vecteurs et sont de même longueur
+% - les composantes de p sont positives ou nulles et leur somme vaut 1.
+%
+% See also RDISCR.
+%
+% ### Copyright (C) D. Chafaï, 2003-12-06.
+% ### http://www.lsp.ups-tlse.fr/Chafai/agregation.html
+% ### Licence GNU General Public License http://www.gnu.org/copyleft/gpl.html
+%
+
+% On pourrait implémenter cette fonction de la façon suivante :
+%
+% INDICES = find(cumsum(p) >= rand);
+% res = x(INDICES(1));
+% return;
+%
+% Cette méthode est correcte mais inefficace car elle ne tient pas compte de
+% la monotonie de cumsum(p), ce qui entraine des tests inutiles une fois que
+% la valeur critique a été franchie. En jargon, c'est un 'firstmatch' qu'il
+% nous faut, pas un 'matchall'. Le nombre de if impliqués dans find est
+% toujours égal à la taille de ce qu'on lui passe en paramètre.
+%
+% Morale de l'histoire : la brièveté d'un code n'assure pas sa performance !
+% Et l'abscence de if dans un code ne signifie pas qu'il ne fait pas appel
+% indirectement à des if, et encore moins que cela est fait de manière
+% optimale ! La fonction find n'est qu'une boucle for contenant un if.
+%
+% Ci-dessous, nous utilisons une version plus rapide dans le plus pur style
+% for-if avec un nombre de if optimal. On pourrait adapter l'ordre des
+% intervalles testés (et donc l'arbre associéé) aux poids p(i) de façon à
+% tester d'abord les intervalles les plus probables. Est-ce vraiment mieux ?
+% Exercice !
+
+n = length(x); % le nombre d'atomes.
+r = rand; % une réalisation de loi uniforme sur [0,1].
+a = 0; b = p(1); % [a,b] = sous-intervalle de proba p(i) pour l'uniforme.
+for i = 1:n-1 % parcours de tous les sous-intervalles juxtaposés.
+ if ((r >= a) & (r < b))
+ res = x(i);
+ return; % on a trouvé le bon intervalle, on sort.
+ end
+ a = b; b = b + p(i+1); % on passe à l'intervalle suivant.
+end
+res = x(n); % le bon intervalle est le dernier.
+return;
diff --git a/Master/texmf-dist/doc/latex/pbsheet/xpl/pgm/rdiscr.m b/Master/texmf-dist/doc/latex/pbsheet/xpl/pgm/rdiscr.m
new file mode 100644
index 00000000000..b3346178e47
--- /dev/null
+++ b/Master/texmf-dist/doc/latex/pbsheet/xpl/pgm/rdiscr.m
@@ -0,0 +1,72 @@
+function X = rdiscr(num,x,p)
+%X = RDISCR(num,x,p)
+% Input num positive integer or a vector [lig,col] of integers
+% x vector of real numbers (support points in IR)
+% p vector of probability weights associated to x
+% i.e. non-negative real numbers such that sum(p) == 1
+% Output X num-vector or a num-matrix of random numbers
+% chosen from the finite discrete distribution on
+% x(1),...,x(n) with probability weights p(1),...,p(n)
+% where n == length(x) == length(p)
+%
+% Renvoie num réalisations ou une matrice [lig,col] de réalisations
+% pseudo-i.i.d de la loi discrète à support fini sur IR dont les
+% points de support sont les composantes du vecteur x, et les poids sont les
+% composantes du vecteur p. Donc x(i) a une probabilité p(i) d'être renvoyé.
+%
+% La méthode consiste à écrire l'intervalle [0,1] comme une réunion disjointe
+% d'intervalles de longueurs p(1),..., p(n) puis à regarder au quel appartient
+% la réalisation d'une loi uniforme obtenue par un appel à rand. Les valeurs
+% renvoyées par des appels successifs sont donc pseudo-indépendantes.
+% Pour des raisons d'efficacité, les conditions nécessaires suivantes ne sont
+% pas contrôlées par cette fonction :
+% - le nombre de paramètres passés est exactement 3
+% - les deux paramètres x et p sont bien des vecteurs et sont de même longueur
+% - les composantes de p sont positives ou nulles et leur somme vaut 1
+% - le paramètre num est un entier positif non nul une un couple de ce type
+%
+% See also PROBADIS.
+%
+% ### Copyright (C) D. Chafaï, 2003-12-06.
+% ### http://www.lsp.ups-tlse.fr/Chafai/agregation.html
+% ### Licence GNU General Public License http://www.gnu.org/copyleft/gpl.html
+%
+
+% Voir les commentaires dans le code de la fonction probadis.
+% Faire 'type probadis' pour cela.
+% Le code qui suit pourrait beaucoup gagner en rapidité sur une machine //
+% Il est possible de l'améliorer en stockant un arbre construit avec les
+% tests utilisés par les valeurs déjà générées. Il est surtout aussi possible
+% d'imiter le code matriciel de la fonction de répartition inverse binomiale
+% de la fonction qbinom de Stixbox, appelée par rbinom. Exercice !
+%
+% D'autres algorithmes sont possibles. Par exemple, on pourrait procéder
+% avec des réalisations de Bernoulli i.i.d. (obtenues facilement avec rand)
+% pour choisir l'intervalle :
+% La probabilité d'être <= x(1) est p(1)
+% Sinon, la probabilité d'être <= x(2) est p(2)/sum(p(2:n))
+% etc. Nul besoin de commencer par x(1), et l'on peut adapter l'arbre utilisé
+% aux poids p(i) de façon à faire un nombre de tests optimal. Exercice !
+
+if length(num) == 1
+ num = [num 1];
+else
+ num = reshape(num,1,2);
+end
+
+n = length(x); % le nombre d'atomes.
+U = rand(num); % réalisations de loi uniforme sur [0,1].
+X = repmat(x(n),num(1),num(2)); % par défaut, la valeur est la plus grande
+for l = 1:num(1) % lignes
+for c = 1:num(2) % colonnes
+ a = 0; b = p(1); % [a,b] = sous-inter. de proba p(i) pour l'uniforme.
+ for i = 1:n-1 % parcours de tous les sous-intervalles juxtaposés.
+ if ((U(l,c) >= a) & (U(l,c) < b))
+ X(l,c) = x(i);
+ break; % on a trouvé le bon intervalle, on sort.
+ end
+ a = b; b = b + p(i+1); % on passe à l'intervalle suivant.
+ end
+end
+end
+return;
diff --git a/Master/texmf-dist/doc/latex/pbsheet/xpl/pgm/rint.m b/Master/texmf-dist/doc/latex/pbsheet/xpl/pgm/rint.m
new file mode 100644
index 00000000000..9e8dd3c8502
--- /dev/null
+++ b/Master/texmf-dist/doc/latex/pbsheet/xpl/pgm/rint.m
@@ -0,0 +1,25 @@
+function X = rint(num,k);
+% X = RINT(num,k)
+% Input num positive integer or a vector [lig,col] of integers
+% k positive integer
+% Output X num-vector or a num-matrix of random numbers
+% chosen from uniform distribution on {1,...,k}
+%
+% Renvoie num réalisations ou une matrice [lig,col] de réalisations
+% pseudo-indépendantes de la loi uniforme discrète sur les k premiers
+% entiers non nuls {1,...,k}.
+%
+% La méthode consiste à considérer la partie entière de 1+kU où U suit une loi
+% uniforme sur [0,1]. Cette dernière s'obtient via la fonction rand, et les
+% valeurs renvoyées par des appels successifs sont donc pseudo-indépendantes.
+%
+% ### Copyright (C) D. Chafaï, 2003-12-06.
+% ### http://www.lsp.ups-tlse.fr/Chafai/agregation.html
+% ### Licence GNU General Public License http://www.gnu.org/copyleft/gpl.html
+%
+
+if length(num) == 1
+ num = [num 1];
+end
+X = ceil(k * rand(num));
+return;
diff --git a/Master/texmf-dist/doc/latex/pbsheet/xpl/pgm/simbin.m b/Master/texmf-dist/doc/latex/pbsheet/xpl/pgm/simbin.m
new file mode 100644
index 00000000000..f9c618a8a69
--- /dev/null
+++ b/Master/texmf-dist/doc/latex/pbsheet/xpl/pgm/simbin.m
@@ -0,0 +1,55 @@
+%
+% ### Copyright (C) D. Chafaï, 2003-12-06.
+% ### http://www.lsp.ups-tlse.fr/Chafai/agregation.html
+% ### Licence GNU General Public License http://www.gnu.org/copyleft/gpl.html
+%
+% Ce bout de code permet de simuler une loi binomiale B(n,p) et de comparer
+% graphiquement les moyennes empiriques avec la moyenne théorique.
+% Tous les vecteurs sont des vecteurs ligne.
+%
+% Nota bene : la bibliothèque Stixbox fournit la fonction rbinom qui permet
+% de s'affranchir des calculs détaillés ici, cf. fin du présent fichier.
+%
+clear r n p q P Q C B X
+clf
+%
+r = input('Nombre maximal de réalisations ? = ');
+n = input('Taille n de la loi binomiale B(n,p), qui a n+1 atomes ? = ');
+p = input('Valeur du paramètre p de la loi binomiale B(n,p) ? = ');
+% p = proba de gagner à pile ou face = proba de 1 dans la Bernoulli sur {0,1}
+% q = proba de perdre à pile ou face = proba de 0 dans la Bernoulli sur {0,1}
+% B(n,p) est la loi de la somme de n v.a. i.i.d. de Bernoulli de ce type,
+% i.e. la nième puissance de convolution de cette loi de Bernoulli. Elle
+% représente la loi du nombre de succés à pile ou face en n lancés.
+%
+disp(sprintf('Calcul de la loi binomiale B(%d,%f)',n,p))
+q = 1 - p;
+P = [1 , cumprod(p * ones(1,n))]; % puissances croissantes de p
+Q = [fliplr(cumprod(q * ones(1,n))), 1]; % puissances décroissantes de q
+C = [1 , cumprod([n:-1:1]) ./ cumprod([1:n])]; % coef. du binôme de i = 1 à n
+B = C .* P .* Q; % vecteur des poids de B(n,p)
+%
+disp(sprintf('Génération aléatoire de %d réalisations de B(%d,%f)',r,n,p))
+X = rdiscr([1,r],[0:n],B); % échantillonnage
+% alternative :
+%X=[]
+%for i=1:r
+% X = [X probadis([0:n],B)];
+%end
+%
+disp(sprintf('Tracé des graphique.'))
+plot(cumsum(X) ./ [1:length(X)],'b') % tracé des moyennes empiriques
+title('Loi des Grands Nombres')
+xlabel('Nombre de realisations')
+ylabel('Moyennes empiriques')
+hold on
+plot(n * p * ones(1,r),'r--') % tracé de la moyenne théorique
+legend('Empirique','Theorique')
+hold off
+%
+% Avec Stixbox, inutile de calculer B et d'appeler rdiscr([1,r],[0:n],B)
+% puisque qu'un simple rbinom([1,r],n,p) suffit.
+% Même si l'on décide d'utiliser quand même prodadis, les coefficients
+% binomiaux nécessaires au calcul de B peuvent se calculer beaucoup plus vite
+% en utilisant la fonction Stixbox bincoef qui fait appel à la fonction gamma.
+%
diff --git a/Master/texmf-dist/doc/latex/pbsheet/xpl/xpl-fr.bib b/Master/texmf-dist/doc/latex/pbsheet/xpl/xpl-fr.bib
new file mode 100644
index 00000000000..076f05db048
--- /dev/null
+++ b/Master/texmf-dist/doc/latex/pbsheet/xpl/xpl-fr.bib
@@ -0,0 +1,39 @@
+@book{barbe-ledoux,
+ AUTHOR = {Barbe, Ph. and Ledoux, M.},
+ TITLE = {Probabilit{\'e}s},
+ YEAR = {1998},
+ PAGES = {262},
+ PUBLISHER = {Belin},
+ SERIES = {De la licence {\`a} l'agr{\'e}gation},
+ ISBN = {2-7011-2131-0}
+}
+
+@book{dacunha-castelle-duflo,
+ AUTHOR = {Dacunha-Castelle, D. and Duflo, M.},
+ TITLE = {Probabilit{\'e}s et statistiques. {T}ome 1},
+ NOTE = {Probl{\`e}mes {\`a} temps fixe.},
+ PUBLISHER = {Masson},
+ ADDRESS = {Paris},
+ YEAR = {1982},
+ PAGES = {xii+214},
+ ISBN = {2-225-74547-1},
+}
+
+@Book{bouleau,
+ AUTHOR = {Bouleau, N.},
+ TITLE = {Probabilit{\'e}s de l'ing{\'e}nieur,
+ variables al{\'e}atoires et simulation},
+ PUBLISHER = {Hermann},
+ YEAR = {1986}
+}
+
+@Incollection{ycart,
+ AUTHOR = {Ycart, B.},
+ TITLE = {{M}od\`eles et {A}lgorithmes {M}arkoviens},
+ PUBLISHER = {Springer},
+ EDITOR = {{S}oci\'et\'e de {M}ath\'ematiques
+ {A}ppliqu\'ee et {I}ndustrielles},
+ YEAR = {2002},
+ SERIES = {Math\'ematiques et {A}pplications},
+ VOLUME = {39}
+}
diff --git a/Master/texmf-dist/doc/latex/pbsheet/xpl/xpl-fr.pdf b/Master/texmf-dist/doc/latex/pbsheet/xpl/xpl-fr.pdf
new file mode 100644
index 00000000000..515b9938826
--- /dev/null
+++ b/Master/texmf-dist/doc/latex/pbsheet/xpl/xpl-fr.pdf
Binary files differ
diff --git a/Master/texmf-dist/doc/latex/pbsheet/xpl/xpl-fr.tex b/Master/texmf-dist/doc/latex/pbsheet/xpl/xpl-fr.tex
new file mode 100644
index 00000000000..2b5e04e387a
--- /dev/null
+++ b/Master/texmf-dist/doc/latex/pbsheet/xpl/xpl-fr.tex
@@ -0,0 +1,146 @@
+\documentclass{pbsheet}
+
+\TITRE{Feuille de TP n°1 -- Initiation à Matlab}
+\FORMATION{Préparation à l'épreuve de modélisation
+ - Agrégation Externe de Mathématiques}
+\ETABLISSEMENT{Université de l'Anonyme XXII}
+\ANNEE{2004}
+\MEL{agreg@labo.univ.fr}
+\AUTEUR{A. Grégatif}
+\WEB{http://www.labo.univ.fr/}
+\DATE{\today}
+
+\begin{document}
+
+Ce TP porte sur les entrées et sorties, les fonctions et les outils
+graphiques dont vous disposez sous Matlab.
+
+\section{Entrées et sorties}
+
+La commande \texttt{input} permet de demander à l'utilisateur Matlab d'entrer
+les valeurs de variables à utiliser. La commande \texttt{pause} permet de
+stopper l'exécution Matlab. Vous pouvez préciser le nombre de secondes de pose
+ou revenir à Matlab en appuyant sur n'importe quelle touche. La commande
+\texttt{save} permet de sauvegarder dans un fichier, dont le nom par défaut
+est \texttt{matlab.mat}, le contenu de certaines variables dont vous souhaitez
+garder une trace. Ce fichier peut être appelé par la commande \texttt{load}
+qui restaure toutes les variables que vous avez sauvegardées.
+
+\begin{lstlisting}[language=Matlab]{Créations et Sauvegardes sous Matlab}
+n=input('Entrez la valeur de n : '); % Affectez une valeur à n.
+a=input('Precisez la valeur de a : '); % Affectez une valeur à a.
+v=a.^[0:n]; A=toeplitz(v); d=det(A); % Création de la matrice de Toeplitz A
+save restoep n a A d; % Sauvegarde de n, a, A, d dans restoep.mat
+clear % Efface toutes les variables de la session.
+load restoep % Restaure les variables de restoep.mat.
+who % Vérification.
+\end{lstlisting}
+
+\section{Fonctions}
+
+Un ensemble de commandes Matlab peut être considéré comme une fonction. On
+peut voir une fonction comme un sous-programme Matlab dont les paramètres
+éventuels sont les arguments de la fonction et dont les résultats sont les
+images de cette fonction. Beaucoup de fonctions Matlab, comme par exemple
+\texttt{mean}, sont déjà écrites en Matlab et le code Matlab correspondant est
+stocké dans un fichier dont le nom se termine par \texttt{.m}. Pour
+\texttt{mean}, il s'agit de \texttt{mean.m}. Ajouter de nouvelles fonctions à
+Matlab revient donc à écrire de nouveaux fichiers de ce type. Il est d'usage
+d'appeler une fonction du même nom que le fichier correspondant.
+
+\textbf{Simulation de lois discrètes.} Dans votre répertoire personnel, éditer
+le fichier \texttt{probadis.m} suivant dont le code Matlab génère une
+réalisation aléatoire d'une loi discrète à support fini.
+
+\MFILE{probadis}
+
+La commande Matlab \texttt{type} permet de lister le contenu d'un fichier.
+Ainsi, \texttt{type probadis} vous montrera le code source Matlab de la
+fonction \texttt{probadis}. Le commentaire ajouté à partir de la seconde ligne
+constituera l'aide affiché lorsque l'utilisateur tapera \texttt{help
+ probadis}. Finalement, la commande \texttt{what} liste les fichiers Matlab
+du répertoire courant.
+
+Voici une autre fonction de simulation de loi discrète, qui peut renvoyer une
+matrice de réalisations.
+
+\MFILE{rdiscr}
+
+\begin{exo}[Loi binomiale]
+ Créer un code Matlab permettant de générer un vecteur aléatoire $X$
+ contenant $N$ réalisations i.i.d. de loi binomiale $\cB(n,p)$ où les valeurs
+ $N,n\geq 1$ et $0<p<1$ sont affectées par l'utilisateur. Pour $N$ assez
+ grand, vérifier la LGN sur les moyennes empiriques successives de $X$. Voici
+ un exemple de programme qui fait l'affaire, et donc la sortie graphique se
+ trouve en page \pageref{fi:simbin}.
+\end{exo}
+
+\MFILE{simbin}
+
+\begin{exo}
+ Soit $(X_n)_{n\in\dN}$ une suite de variables aléatoires i.i.d. de loi
+ exponentielle $\cE(\lambda)$ avec $\lambda >0$. Si $S_n=\sum_{k=1}^n X_k$,
+ $N_0=0$ et pour tout $t> 0$, $N_t=\sum_{n=1}^\infty \rI_\BRA{S_n\leq t}$,
+ $(N_t)_{t\geq0}$ est un processus de Poisson d'intensité $\lambda$. Montrer
+ que, pour tout $t>0$, $N_t$ suit la loi de Poisson $\cP(\la t)$. En déduire
+ un code Matlab permettant de générer un vecteur aléatoire $Y$ contenant $N$
+ réalisations i.i.d. de loi $\cP(\la)$ où les valeurs $N\geq 1$ et $\la>0$
+ sont affectées par l'utilisateur. Pour $N$ assez grand, vérifier la LGN sur
+ les moyennes empiriques successives de $Y$.
+\end{exo}
+
+\begin{exo}
+ Pour $N$, $N_1$ et $n \geq 1$ avec $N_1,n \leq N$, la loi hypergéométrique
+ $\cH(N,N_1,n)$ est donnée, pour tout $k \in \dN$ avec $0\leq k \leq n$, par
+ $\dP(X=k)=C_{N_1}^kC_{N-N_1}^{n-k}/C_N^n$. Créer un code Matlab permettant
+ de générer un vecteur aléatoire $Z$ contenant $M$ réalisations i.i.d. de loi
+ $\cH(N,N_1,n)$ où les valeurs $M, N \geq 1$ et $N_1,n\leq N$ sont affectées
+ par l'utilisateur.
+ \begin{enumerate}
+ \item Si $N$ tend vers l'infini et le rapport $N_1/N$ tend vers $p$ avec
+ $0<p<1$, montrer que $X$ converge en loi vers la loi Binomiale $\cB(n,p)$.
+ Pour $M, N$ assez grand et $N_1=pN$ avec $0<p<1$, tracer l'histogramme de
+ $Z$ et comparer le à la loi $\cB(n,p)$.
+ \item Si $N$, $N_1$ et $n$ tendent vers l'infini et le produit $nN_1/N$ tend
+ vers $\la>0$, montrer que $X$ converge en loi vers la loi de Poisson
+ $\cP(\la)$. Pour $M$, $N$ assez grand, $N_1=\la\sqrt{N}$ et $n=\sqrt{N}$,
+ tracer l'histogramme de $Z$ et comparer le à la loi $\cP(\la)$.
+ \end{enumerate}
+\end{exo}
+
+\section{Représentations graphiques}
+
+\begin{lstlisting}[language=Matlab]
+ {Illustration de la LGN pour la loi exponentielle}
+ clear; n=1000; lambda=0.5; X=-log(rand(n,1))/lambda;
+ figure; % Création d'une nouvelle fenêtre graphique.
+ plot(cumsum(X)'./[1:length(X)],'b') % Trace les moy. emp. successives de X.
+ title('Loi des Grands Nombres') % Titre de la figure.
+ xlabel('Nombre de réalisations') % Titre des abscisses.
+ ylabel('Moyennes empiriques') % Titre des ordonnées.
+ hold on % Garde la fenêtre graphique.
+ plot(1/lambda*ones(n,1),'r--'); % Trace la limite théorique.
+ legend('Empirique','Theorique'); % Légende.
+\end{lstlisting}
+
+\begin{exo}
+ Ajouter à vos codes Matlab les représentations graphiques rencontrées
+ ci-dessus.
+\end{exo}
+
+\FIG{simbin}{1.0}{htbp}{Sortie graphique du programme \ref{code:simbin}
+ \pageref{code:simbin}.}
+
+Voici une fonction Matlab qui permet de simuler la loi uniforme discrète finie
+de façon rapide et simple.
+
+\MFILE{rint}
+
+\nocite{*}
+
+\phantomsection % Nécessaire pour le PDF.
+\addcontentsline{toc}{section}{Bibliographie}
+\bibliographystyle{amsalpha}
+\bibliography{xpl-fr}
+
+\end{document}