Consider a renewal process whose interarrival distribution F is a mixture of two exponentials. That is, F(x) = pe* + qe,q=1-p Compute the renewal function E[N(t)]. Hint Imagine that at each renewal a coin, having probability p of landing heads, is flipped If heads appears, the next interarrival is exponential with rate A,, and if tails, it is exponential with rate A Let R(t) = i if the exponential rate at time t is A, Then:

(a) determine P{R(t) = i}, i = 1, 2,

(b) argue that E [N(t)] = ^, f' P{R(s) = i} ds = E where A(s) = R(s)- 1=1 E [S, A(s) ds] -