easy Probability
A release-checked easy problem for training Conditional Expectation, Linearity of Expectation, Uniform, Expected Value/LOTUS.
$n$ people each have an amount of money in their wallets that are IID $\unif{0}{1}$ random variables. The person who has the most money in their wallet receives the money from everyone's wallet. If you are person $1$ and see $\$x_1$ in your wallet, what is your estimate of the total amount of money among everyone's wallet? Report the answer when $x_1 = 0.75$ and $n = 15$.
This Probability problem is tagged Conditional Expectation, Linearity of Expectation, Uniform, Expected Value/LOTUS. State the random variables and conditioning information explicitly, then check the result against boundary cases before opening hints or a solution.
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