1 Certain computing service center in a pharmaceutical compa

1. Certain computing service center in a pharmaceutical company defines a severe power outage as a power failure lasting longer than their uninterruptable power supply (UPS) equipment can maintain power. During the course of a year the number of severe power outages, K, is a geometric random variable given by 2 (3* pK (k Accordingly, the probability of having no severe power outages during the course of a year is 2/5. (a) 10 points The board of directors of the company is considering a compensation scheme which would make no payment over the year if the number of severe power outages were zero or one, but which would pay the computing service center $2000 for every such outage (including the first if the total number of severe power outages in a year were two or more. Determine the expected annual sum that the computing service center would receive. (b) [10 points] To what value would the parameter of the geometric distribution have to be changed (from 2/5) for the expected annual sum to be $1500?

Solution

Mean of the geometric distribution = 1/p = 2.5

a) Let X be the no of power outage

x 0 1 2 3 ......

charges = 2000x

Expected value of sum = E(2000x) = 2000(2/5) = 800

b) If Expected value of sum is to be 1500 = 2000p

Hence p should be 1500/2000 =3/4

Thus parameter should be changed from 2/5 to 3/4