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Unformatted text preview: = 1 9 (c) What is the pmf of X ? p k = P [ X = k ] = 1 ... k1 1 2 ... k p k 1 2 3 4 p k = P ( X = k ) 1 9 2 9 2 9 2 9 2 9 1 (d) What is the (large t ) expected # of jobs in the system? E [ X ] = 0 p + 1 p 1 + 2 p 2 + 3 p 3 + 4 p 4 = 0 1 9 + 2 9 (1 + 2 + 3 + 4) = 20 / 9 (d) What is the probability that an incoming in message is turned away? An incoming message is lost when system is full i.e., X = 4 P (message lost) = P (system full) = P ( X = 4) = p 4 = 2 / 9 (e) What is the expected number of messages in the buffer? Let Y = # of messages in the buer; note that Y is a function of X X 1 2 3 4 Y 1 2 p k 1 9 2 9 2 9 2 9 2 9 E [ Y ] = 0 p + 1 p 1 + 2 p 2 + 3 p 3 + 4 p 4 = 0 1 9 + 0 2 9 + 0 2 9 + 1 2 9 + 2 2 9 = 5 / 9 2...
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This note was uploaded on 02/01/2012 for the course STAT 330B taught by Professor Zhou during the Spring '11 term at Iowa State.
 Spring '11
 Zhou

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