The Gamma distribution with paramters
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fa,f (x) =Fox -e Oxfor allx 2 0.The I function is defined byT (s) =xtte * dx.As usual, the constant- is a normalization constant that gives ffa,, (x) dx = 1.In this problem, let X1, …, Xn be i.i.d. Gamma variables withB = -for some a > 0.That is, X1, …, Xn ~ Gamma (a, . random variables for some a > 0. The pdf for X; is therefore1fa (x) =T(a)ga x -e x/a,for all x 2 0.