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Unformatted text preview: STAT/MA 416 October 24, 2011 Problem Set 24 Name: 1. Consider a pair of random variables X,Y with constant joint density on the triangle with vertices at (0 , 0), (3 , 0), and (0 , 3). a. For 0 ≤ y ≤ 3, find the conditional density f X  Y ( x  y ) of X , given Y = y . b. Find the conditional probability that X ≤ 1, given Y = 1. I.e., find P ( X ≤ 1  Y = 1). c. Find the conditional probability that X ≤ 1, given Y ≤ 1. I.e., find P ( X ≤ 1  Y ≤ 1). 1 2. Consider a pair of random variables X,Y with constant joint density on the quadrilateral with vertices (0 , 0), (2 , 0), (2 , 6), (0 , 12). a. For 0 ≤ y ≤ 6, find the conditional density f X  Y ( x  y ) of X , given Y = y . b. For 6 ≤ y ≤ 12, find the conditional density f X  Y ( x  y ) of X , given Y = y . c. Find the conditional probability that X ≤ 1, given 3 ≤ Y ≤ 9. I.e., find P ( X ≤ 1  3 ≤ Y ≤ 9)....
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This note was uploaded on 02/28/2012 for the course STAT 416 taught by Professor Staff during the Fall '08 term at Purdue.
 Fall '08
 Staff
 Probability

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