medium Probability
A release-checked medium problem for training Uniform, Expected Value/LOTUS, Tail Sum/Integral, Geometric Probability.
$n$ points are independently selected uniformly at random from the interior of the square centered at the origin with vertices at $(\pm 1,\pm 1)$. Find the expected area of the smallest square centered at the origin that contains all $n$ points when $n = 9$.
This Probability problem is tagged Uniform, Expected Value/LOTUS, Tail Sum/Integral, Geometric Probability. 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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