Assume that the length of telephone calls T in minutes is described by the distribution with pdf (a) Find E(T) and Var(T). (b) Let S = T1 + T2 + ••• + Tn' where the Ti are independent random variables...

Assume that the length of telephone calls T in minutes is described

by the distribution with pdf

(a) Find E(T) and Var(T).

(b) Let S = T1 + T2 + ••• + Tn' where the Ti are independent

random variables with the distribution given by f(t). Find

E(S) and Var(S). (These will be functions of n.)

(c) Find the probability that the total length of 100 calls

does not exceed 4 hr (T is assumed to be measured in minutes).

Note that (S - E(S))/11/ar(S) is approximately a standard

normal variable.