Hw07 - STAT 410 Homework #7 (due Friday, March 7, by 3:00...

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STAT 410 Spring 2008 Homework #7 (due Friday, March 7, by 3:00 p.m.) 1. Suppose X has a multivariate normal N 3 ( μ , Σ ) distribution with mean μ = ± ² ³ ³ ³ ´ µ 23 17 7 and covariance matrix Σ = ± ² ³ ³ ³ ´ µ - - 25 10 0 10 9 2 0 2 4 . a) Find P ( X 1 > 10 ). b) Find P ( X 1 > 10 | X 2 = 20, X 3 = 25 ). c) Find P ( X 2 < 20 ). d) Find P ( X 2 < 20 | X 1 = 10, X 3 = 20 ). e) Find P ( 3 X 1 + 2 X 2 + X 3 > 60 ). 2. Let X be a random variable with a Gamma distribution with α = 3 and θ = 5 ( i.e., λ = 0.2 ). Find the probability P ( X > 31.48 ) … a) … by integrating the p.d.f. of the Gamma distribution; b) … by using the relationship between Gamma and Poisson distributions; Hint: If X has a Gamma ( α , θ = 1 / λ ) distribution, where α is an integer, then F X ( t ) = P ( X t ) = P ( Y α ), where Y has a Poisson ( λ t ) distribution. c)
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This note was uploaded on 02/11/2011 for the course STAT 410 taught by Professor Monrad during the Spring '08 term at University of Illinois, Urbana Champaign.

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Hw07 - STAT 410 Homework #7 (due Friday, March 7, by 3:00...

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