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author | Karl Berry <karl@freefriends.org> | 2017-07-13 23:06:59 +0000 |
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committer | Karl Berry <karl@freefriends.org> | 2017-07-13 23:06:59 +0000 |
commit | 03542c01781307bd8cb29571d8a39197a4de83e2 (patch) | |
tree | b11e221ce28f24eee3995a8efb51d2e76993472c /Master/texmf-dist/doc/latex/probsoln/samples/prob-probspaces2.tex | |
parent | 04f93eb1202717fcb407f1271d28f4153aaa0ca0 (diff) |
probsoln (10jul17)
git-svn-id: svn://tug.org/texlive/trunk@44783 c570f23f-e606-0410-a88d-b1316a301751
Diffstat (limited to 'Master/texmf-dist/doc/latex/probsoln/samples/prob-probspaces2.tex')
-rw-r--r-- | Master/texmf-dist/doc/latex/probsoln/samples/prob-probspaces2.tex | 43 |
1 files changed, 43 insertions, 0 deletions
diff --git a/Master/texmf-dist/doc/latex/probsoln/samples/prob-probspaces2.tex b/Master/texmf-dist/doc/latex/probsoln/samples/prob-probspaces2.tex new file mode 100644 index 00000000000..dacddb510cf --- /dev/null +++ b/Master/texmf-dist/doc/latex/probsoln/samples/prob-probspaces2.tex @@ -0,0 +1,43 @@ + % This file is public domain + % + % Finite probability spaces +\begin{defproblem}{weightedcoin} +\begin{onlyproblem}% +A coin is weighted so that heads is four times as likely +as tails. Find the probability that: +\begin{textenum} +\item tails appears, +\item heads appears +\end{textenum} +\end{onlyproblem} +\begin{onlysolution}% +Let $p=P(T)$, then $P(H)=4p$. We require $P(H)+P(T)=1$, +so $4p+p=1$, hence $p=\frac{1}{5}$. Therefore: +\begin{textenum} +\item $P(T)=\frac{1}{5}$, +\item $P(H)=\frac{4}{5}$ +\end{textenum} +\end{onlysolution} +\end{defproblem} + +\begin{defproblem}{validprobspaces} +\begin{onlyproblem}% +Under which of the following functions does +$S=\{a_1,a_2\}$ become a probability space? +\par +\begin{textenum} +\begin{tabular}{ll} +\item $P(a_1)=\frac{1}{3}$, $P(a_2)=\frac{1}{2}$ +& +\item\label{validprobspacescorrect1} $P(a_1)=\frac{3}{4}$, $P(a_2)=\frac{1}{4}$ +\\ +\item\label{validprobspacescorrect2} $P(a_1)=1$, $P(a_2)=0$ +& +\item $P(a_1)=\frac{5}{4}$, $P(a_2)=-\frac{1}{4}$ +\end{tabular} +\end{textenum} +\end{onlyproblem}% +\begin{onlysolution}% +\ref{validprobspacescorrect1} and \ref{validprobspacescorrect2}% +\end{onlysolution} +\end{defproblem} |