Lecture28(11-05-2008) - 36-225 Handout for Lecture # 28...

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Unformatted text preview: 36-225 Handout for Lecture # 28 November 5, 2008 1. Suppose that the joint pdf of (X, Y ) is given by: 1 (xy + 1) 80 0<x<4 0<y<4 otherwise fXY (x, y) = 0 (a) Show that fXY (x, y) is a legitimate density function. (b) Find P (X 1, Y 1) 2. A nut company markets cans of deluxe mixed nuts containing almonds, cashews and peanuts. Let X and Y represent the proportion of almonds and cashews respectively. Suppose that the joint pdf of (X, Y ) is given by: 24xy fXY (x, y) = x > 0, y > 0 x+y 1 otherwise 0 What is the probability that almonds and cashews together make-up at most 50% of the can (and so you feel cheated....). 3. Suppose that the joint pdf of (X, Y ) is given by: 6e-(2x+3y) fXY (x, y) = x>0 y>0 otherwise 0 (a) Show that fXY (x, y) is a legitimate density function. (b) Find P (X < Y ) ...
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This note was uploaded on 05/16/2011 for the course STATISTICS 225 taught by Professor Finegold during the Spring '11 term at Carnegie Mellon.

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