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Unformatted text preview: i, j ∈ { 1 , 2 , 3 } elsewhere. (a) Find the value of the constant k . (b) Calculate P ( X = 1 , Y < 3), P ( X = 1 , Y ≤ 3), P ( X = 2), P ( X < Y ), P ( X ≤ Y ). 6. Let the joint PMF of discrete RVs X and Y be p ( i, j ) = b k ( i 2 + j 2 ) if ( i, j ) ∈ { (1 , 1) , (1 , 3) , (2 , 3) } elsewhere. (a) Find the value of the constant k . (b) Find the marginal PMFs of X and Y . 7. The joint probability density function of random variables X and Y is given by f ( x, y ) = b 2 if 0 ≤ y ≤ x ≤ 1 0 elsewhere. (a) Calculate the marginal PDFs of X and Y . (b) Calculate P ( X < 1 / 2), P ( X < 2 Y ), and P ( X = Y ). 2 8. On a line segment AB of length l , two points C and D are placed at random and independently. What is the probability that C is closer to D than to A ? 9. Two RVs X and Y are jointly uniform on [0 , 1] 2 . Calculate the probability P ( Y ≤ X and X 2 + Y 2 ≤ 1). 3...
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This note was uploaded on 09/30/2009 for the course ECSE 305 taught by Professor Champagne during the Spring '09 term at McGill.
 Spring '09
 Champagne

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