STAT 238 Final, Fall 2004

AMERICAN UNIVERSITY OF BEIRUT STATISTICS 238, Final Exam Jan 24, 2005 Time = 1 Hour and 30 Minutes You are allowed to use a formula sheet. . Some numbers are selected at random from s table of random numbers containing integers 1 to m inclusive. The system is said to be in state j if the largest integer selected number is j, for j=1,---,m. Compute PR. . My house uses two light bulbs. On the average, a light bulb lasts 22 days (exponentially distributed). When a light bulb burns out, it takes me on the average of 2 days (exponentially distributed) before I replace it. What is the average number of working light bulbs? . The Birth and Death process with A; = 0 for j > 0 and yj = y for j > 0 is called a pure death process. Find P,;(t). . The Birth and Death process with A; = jA for 7 > 0 and pj; = 0 for j > 0 is called a linear birth process. Find P,;(t).