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\section*{CS 70 homework 10 submission}
Your full name: PUT YOUR NAME HERE
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Your login name: PUT YOUR LOGIN NAME HERE
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Homework 10
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Your section number: PUT YOUR SECTION NUMBER HERE
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Your list of partners: LIST THE PEOPLE YOU WORKED WITH HERE (OR ``none'')
\begin{enumerate}
\item
\begin{enumerate}[{(}a{)}]
\item Which of the two airlines has a better chance of
arriving on time into Los Angeles?
YOUR ANSWER GOES HERE
\item Which of the two airlines has a better chance of
arriving on time into Chicago?
YOUR ANSWER GOES HERE
\item Which of the two airlines has a better chance of
arriving on time overall?
YOUR ANSWER GOES HERE
\item Explain the apparent paradox intuitively.
YOUR ANSWER GOES HERE
\item Interpret this in terms of conditional probabilities.
If $\Pr[A|E]>\Pr[B|E]$ and $\Pr[A|\overline{E}]>\Pr[B|\overline{E}]$,
are we guaranteed that $\Pr[A] > \Pr[B]$?
YOUR ANSWER GOES HERE
\end{enumerate}
\item
Is this game a good deal for Alice? Explain.
YOUR ANSWER GOES HERE
\item
\begin{enumerate}[{(}a{)}]
\item If $n$ is a positive integer, what is $\Pr[D=n]$
(as a simple function of $n$ and $p$)?
YOUR ANSWER GOES HERE
\item If $n$ is a non-negative integer, what is $\Pr[D>n]$
(as a simple function of $n$ and $p$)?
YOUR ANSWER GOES HERE
\item Prove that if $X$ is any random variable that takes values on $\N$,
then $\E[X] = \sum_{n=0}^\infty \Pr[X > n]$.
YOUR ANSWER GOES HERE
\item Calculate the expected time until the light bulb burns
out, namely, $\E[D]$ (as a simple function of $p$).
YOUR ANSWER GOES HERE
\item
What's the expected number of baby girls they will have, before
they have their first baby boy?
YOUR ANSWER GOES HERE
\end{enumerate}
\item
\begin{enumerate}[{(}a{)}]
\item
Find the sample space $\Omega$ and identify the value of $X$ for each
sample point $\omega \in \Omega$.
YOUR ANSWER GOES HERE
\item Calculate $\E[X]$. Is the game fair to Charles? Explain.
YOUR ANSWER GOES HERE
\item
Calculate $\E[Y]$. Is this fair to Charles? Explain.
YOUR ANSWER GOES HERE
\item
Suggest a way that you could gain an unfair advantage
so you will win the pot with probability $> 1/n$, where $n$ is the number of
participants in the pool.
YOUR ANSWER GOES HERE
\end{enumerate}
\end{enumerate}
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