easy Probability

Visible Number of Heads

A release-checked easy problem for training Expected Value, Discrete Random Variables.

Question

Suppose $20$ people whose heights follow some unknown continuous distribution are arranged in a single-file line. We then stand at the front of the line and observe that we can see someone's head if they are taller than everyone that comes before. Let $X$ be the number of visible heads. Compute $\mathbb{E}[X]$? Round to the nearest tenths.

Practice focus

This Probability problem is tagged Expected Value, Discrete Random Variables. State the random variables and conditioning information explicitly, then check the result against boundary cases before opening hints or a solution.