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Unformatted text preview: ) = ( n + m 2 ) ( n 2 )( m 2 ) n m ! n/ 2 x n/ 21 1 + n m x !( n + m ) / 2 , x > ,n,m = 1 , 2 ,... then X is called following an F distribution with degrees of freedom n and m , and denoted by X F ( n,m ). 6 5. Suppose X is a random variable with pdf f ( x ) = 1 ex , x > , > (a). Find m.g.f M ( t ) of X . For what values of t does M ( t ) exist ? (b). Find E ( X k ) for a positive integer k . 7 6. (a). Let X be a random varaible with mgf M ( t ) ,h < t <h Prove that P ( X a ) eat M ( t ) , < t < h and P ( X a ) eat M ( t ) ,h < t < (b). Suppose the mgf of X exists for all real values of t and is given by M ( t ) = e tet 2 t , t 6 = 0 M (0) = 1 Show that P ( X 1) = 0 and P ( X 1) = 0...
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This note was uploaded on 06/21/2010 for the course STAT 5023 taught by Professor Yi,graceyun during the Spring '10 term at Waterloo.
 Spring '10
 Yi,GraceYun

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