Suppose that X , time (in minutes) between arrivals of successive customers, is

Question

Suppose that X , time (in minutes) between arrivals of successive customers, is exponentially distributed with = .5. It can be shown that the total time Y that elapses before the nth customer arrives has the gamma distribution with = n and = 1/. (a) How much time can be expected to elapse before the third customer arrives? 6 Correct: Your answer is correct. (b) What is the probability that the third customer (after the one who just arrived) will arrive within the next fourteen minutes? .010 Incorrect: Your answer is incorrect.

Explanation / Answer

here from above parameter =3 and  =2 ; probability that the third customer  will arrive within the next fourteen minutes =P(X<14) =0.97036

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