Question

Consider a homogeneous Poisson process {N(t), t ≥ 0} with rate α. Now color each point blue with probability p and red with probability q = 1 − p. Colors of distinct points are independent.

Let X be the location of the second blue point that comes after the third red point. (That is after the location of the third red point, start counting blue points; the second one is X.) Find E(X).

Answer 1