Question

Problem 5: 10 points Assume that a mumber N of phone calls handled by a customer service representative during one 8-hour shift is Poisson distributed with rate = A = 5 calls per shift. Duration T ofa randomly selected call in minutes is uniformly distributed over the interval (4, 10). Duration values (Th : k = 1,2,.,} do not depend on N. Consider the total time spent on conversations with customers, s-ΣΤ 1. Evaluate expected value of S 2. Determine the variance of S

Answer 1

For Poina):メ~P() P(x E P -ze z=0,\,2, -. - 2eo 2 2-2 - E(X-))+E)- ECx) » X^-^: A E v() E

타T)-J*E,0h..는h.7 -52 VanTE)E() E(S W. E N) . Nan -7n ae Var Vaz 7 ane ECS EE(SN E(7N)7 E( 7^= 7x5 - 35 Von(6E (S+ Von(E(S) E (3N)+ V(TN 3 E6)+49 Van() t 52 x 5 S2 260