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Unformatted text preview: Stat 5101 (Geyer) Fall 2009 Homework Assignment 2 Due Wednesday, September 23, 2009 Solve each problem. Explain your reasoning. No credit for answers with no explanation. 21. Suppose we have a PMF f with domain S (the original sample space), and we have a map g : S that induces a probability model with PMF pr with domain (the new sample space) given by the formula on slide 80. Prove that for any realvalued function h on X h ( )pr( ) = X x S h ( g ( x ) ) f ( x ) 22. Suppose pr is the uniform distribution on = { 2 , 1 , , 1 , 2 } and the random variable X defined by X ( ) = 2 , . Determine the PMF of the random variable X . 23. Suppose X = ( X 1 ,X 2 ) has the uniform distribution on { 1 , 2 , 3 , 4 , 5 , 6 } 2 . (a) Show that the components of X are independent. (b) Determine the PMF of the distribution of the random variable Y = X 1 + X 2 ....
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