Consider N persons each with a distinct height They stand in

Consider N persons, each with a distinct height. They stand in a line and you stand in front of them facing them. You can see a person only if all those standing in front of him or her are shorter than him or her. What is the expected number of persons you would be able to see Assume that the position of each person in the line is random and uniform.

Solution

X : Number of people you can see

X ~ Uniform (1,N)

E(X) = ( N + 1)/2