Question
A uniformly random point is selected from the interior of the unit circle. Let $R_1$ be the distance of the point to the center, and $R_2$ be the (shortest) distance of the point to the circumference. Find $\ev{\min(R_1,R_2)}$.
medium Probability
Radial Measure
A release-checked medium problem for training Uniform, Expected Value/LOTUS, Tail Sum/Integral, Geometric Probability.
Practice focus
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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