A release-checked medium problem for training Expected Value.
Question
Martin is riding his remote control skateboard around campus. Assume his house is the origin $(0,0)$, and that movement to the right is positive horizontally, and movement into campus (upwards) is positive vertically. Each second, Martin uniformly picks a random angle between $0$ and $2\pi$, moving the skateboard 1 foot in that direction. After $16$ seconds, what is the expected squared distance from the origin?
Practice focus
This Probability problem is tagged Expected Value. State the random variables and conditioning information explicitly, then check the result against boundary cases before opening hints or a solution.