1. Let W be an exponential random variable with parameter B unknown. Find the maximum likelihood estimator for B based on a sample of size n. Does it differ from the method of moments estimator?

2. A computer center employs consultants to answer users questions. The center is open from 9 a.m. to 5 p.m. each weekday. Assume that calls arriving at the center constitute a Poisson process with unknown parameter A calls per hour. To estimate A, these observations were obtained on A, the number of calls arriving per hour:

8   6   12   15   12

4   9    7    20   10

(a) Find the maximum likelihood estimate for X.

(b) Estimate the average time of arrival of the first call of the day.