A colleague Bill Wardlaw (March 3, 1936-January 2, 2013) used to create a “Problem of the Week” for his students, giving a prize of a cookie if they could solve it. Here is one of them.
Suppose that you draw numbers from randomly until first exceeds . What is the probability that this happens on the fourth draw? That is, what is the probability that and ?
In the above problem, what is the expected number of draws until the sum first exceeds ?