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Unformatted text preview: 1 Fifth Problem Assignment EECS 401 Problem 1 Discrete random variable X is described by the PMF p X ( x ) = K − x 12 , if x = 0, 1, 2 0, for all other values of x Let D 1 , D 2 , . . . , D N represent N successive independent experimental values of ran- dom variable X . (1) Determine the numerical value of K . (2) Determine the probability that D 1 > D 2 . (3) Determine the probability that D 1 + D 2 + . . . + D N ♼ 1.0 (4) Define R = max ( D 1 , D 2 ) and S = min ( D 1 , D 2 ) . Determine the following PMF’s for all values of their arguments: (a) p S ( s ) (b) P R | S ( r | ) (c) P R,S ( r, s ) (d) P T ( t ) with T = ( 1 + D 1 ) / ( 1 + S ) (5) Determine the expected value and variance of random variable S defined above. (6) Given D 1 + D 2 ♼ 2.0 , determine the conditional expected value and conditional variance of random variable S defined above. Problem 2 A salesman has scheduled two appointments to sell encyclopedias. His first appointment will lead to a sale with probability 0.3, and his second appointment willappointment will lead to a sale with probability 0....
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This note was uploaded on 04/04/2012 for the course ECE 139 taught by Professor Staff during the Spring '08 term at UCSB.
- Spring '08