Assignment5

Assignment5 - 1 Assignment 5, STAT220-Winter 2011...

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1 Assignment 5, STAT220-Winter 2011 Instructor: Kamyar Moshksar Due on April 4th, In class Problem 1 - Let ( X 1 ,X 2 ,X 3 ) Mult( n,p 1 ,p 2 ,p 3 ) . (a)- Compute Cov( X 1 + 3 X 2 ,X 2 + X 3 ) . (b)- Let α be a real number. Determine the value of α such that X 1 and X 2 + αX 3 are uncorrelated. (c)- Calculate ρ X 1 ,X 2 2 . (d)- Write down the formulae for f X 1 ,X 2 | X 1 + X 3 ( .,. | t ) where t R X 1 + X 3 . Problem 2- Let X be a random variable whose moment generating function is M X ( t ) = a 2 - e - t . where a R . (a)- Find a . (b)- Determine values of t R such that the definition for M X ( t ) is meaningful. (c)- Find E ( X ( X 2 + 1)) . (d)- Find f X ( . ) . (e)- Find P ( X is an even number ) . Problem 3 - In this problem we are going to see why the sum of two independent random variables X 1 ∼ N ( μ 1 2 1 ) and X 2 ∼ N ( μ 2 2 2 ) is again a normal random variable. (a)- Recall that for two independent discrete random variables
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This note was uploaded on 01/26/2012 for the course ECON 401 taught by Professor Burbidge,john during the Fall '08 term at Waterloo.

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Assignment5 - 1 Assignment 5, STAT220-Winter 2011...

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