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Unformatted text preview: , 2 , 3 , 4. And the probability of y to take value k is P ( y = k ) = p k . p 1 + p 2 + p 3 + p 4 = 1 ,p k ≥ 0. Let X k be the number of outcomes taking value k . a) Show the joint distribution of X = ( X 1 ,X 2 ,X 3 ,X 4 ). b) Find the joint distribution of ( X 1 ,X 2 ,Y ), where Y = X 3 + X 4 . c) Find the marginal distribution of Y = X 1 + X 2 d)Find the conditional distribution of ( X 1 ,X 2 ) given X 3 ,X 4 . 5. A is a 3x3 matrix 1 2 4 0 2 7 0 0 6 x is a 3x1 vector x = ( x 1 ,x 2 ,x 3 ) T and y is a 3x1 vector (1 , 2 , 3) T . a) Suppose Ax = y , solve for x. b) Derive the matrix A1 . 6. A is a 2x2 matrix ± 1 ρ ρ 1 ² . Find 2x2 upper trianglar matrix U such that UU T = A . 1...
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This note was uploaded on 01/13/2010 for the course STATS 116 taught by Professor Staff during the Spring '07 term at Stanford.
 Spring '07
 Staff
 Probability

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