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Unformatted text preview: Stat 5101 (Geyer) Fall 2011 Homework Assignment 2 Due Wednesday, September 21, 2011 Solve each problem. Explain your reasoning. No credit for answers with no explanation. 21. Suppose we have a PMF f X with domain S (the original sample space), and we have a map g : S T that induces a probability model with PMF f Y with domain T (the new sample space) given by the formula on slide 82. Prove that for any realvalued function h on T X y T h ( y ) f Y ( y ) = X x S h ( g ( x ) ) f X ( x ) 22. Suppose we have the uniform distribution on S = { 2 , 1 , , 1 , 2 } and the random variable X defined by X ( s ) = s 2 , s S. 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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This note was uploaded on 02/07/2012 for the course STAT 5101 taught by Professor Staff during the Fall '02 term at Minnesota.
 Fall '02
 Staff

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