Suppose Yi,Vi, i 1 are independent, with Yi being exponential with rate and Vi being

Suppose Yi,Vi, i ≥ 1 are independent, with Yi being exponential with rate λ and Vi being exponential with rate μ. Let Sn =n i=1(Yi − Vi ), n ≥ 1. For positive constants a and b,

(a) Find Pa, the probability that Sn,n ≥ 1 is greater than a before it is less than

−b.

(b) With N = min(n : Sn ≥ a or Sn ≤−b), find E[N].