The Gamma distribution Gamma ( a , $ ) with paramters a > O , and $ > O is defined by the density* fap ( x ) = 18^ - Too * * - e-#*, for allx 2 0. The I function is defined by [ ( S ) = \\ x `- le - * dix . As Usual , the constant $ It Is a normalization constant that gives / faq ( * ) dx = 1 . In this problem , let * 1 . .... In bei.i.d . Gamma variables with B = - for some a > O . That is ,* * 1 . .... In ~ Gamma ( a , & ) random variables for some a > O . The pof for* ; is therefore* 1 Jalx ) _ _ _^e-^, for all x 2 0