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Unformatted text preview: ) = Î“( n + m 2 ) Î“( n 2 )Î“( m 2 ) Â· Â± n m ! n/ 2 Â· x n/ 21 Â· Â± 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 âˆ¼ F ( n,m ). 6 5. Suppose X is a random variable with pdf f ( x ) = 1 Î² exÎ¼ Î² , x > Î¼,Î² > (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 â‰¥ a ) â‰¤ eat M ( t ) , < t < h and P ( X â‰¤ a ) â‰¤ 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 â‰¥ 1) = 0 and P ( X â‰¤ 1) = 0...
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 Spring '10
 Yi,GraceYun
 Probability distribution, probability density function, Heaviside step function, MGF M

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