hw3 - ORIE 3500/5500 Engineering Probability and Statistics...

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ORIE 3500/5500 – Engineering Probability and Statistics II Fall 2010 Assignment 3 Problem 1 This exercise will be easy for those familiar with the Japanese puzzles called nonograms . The marginal pmfs of discrete random variables X and Y are given in the following table: a i /b j 1 2 3 4 5 p X ( a i ) 1 1/14 2 5/14 3 4/14 4 2/14 5 2/14 p Y ( b j ) 5/14 4/14 2/14 2/14 1/14 1 Moreover, for a i and b j from 1 to 5, the probability P ( X = a i , Y = b j ) is either 0 or 1 / 14. Find the joint pmf of X and Y . Problem 2 A bin of 5 transistors is known to contain 3 that are defective. The transistors are to be tested, one at a time. Denote by N G the number of tests made until the second good transistor is spotted, and by N D the number of tests until the second defective transistor is spotted. Find the joint probability mass function of N G and N D . Problem 3 The joint pdf of X and Y is given by f X,Y ( x, y ) = Cx (3 - 2 Cy ) , 0 x 1 , 0 y 2 , where C is an unknown constant.
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