Unformatted text preview: (a) Find P A , the probability that A is still in service when you move over to server 2. (b) Find P B , the probability that B is still in the system when you move over to server 2. (c) Find E [ T ] , where T is the time that you spend in the system. Hint: Write T = S 1 + S 2 + W A + W B where S i is your service time at server i , W A is the amount of time you wait in queue while A is being served, and W B is the amount of time you wait in queue while B is being served. 3. (Chapter 3 Problem #42 of the textbook.) A total of 11 people, including you, are invited to a party. The times at which people arrive at the party are independent uniform (0 , 1) random variables. (a) Find the expected number of people who arrive before you. (b) Find the variance of the number of people who arrive before you. 4. A fair die is rolled repeatedly. Let T 54 = the number of rolls until the numbers 5 and 4 ﬁrst appear consecutively in that order. Find E [ T 54 ] . 1...
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 Fall '08
 Chisholm
 Probability

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