Question: Please see the problem in the attachment. Let X be a gamma random variable with parameter a and 3. The PDF of X is given

Please see the problem in the attachment.

Let X be a gamma random variable with parameter a and 3. The PDF of X is given by Ba fx (20 ) = Tax-e-3x x> 0 0 x 0 and B > 0, and T(a) = / ta-le tat is a normalization constant. Show that MGF of X is given by Mx(s) S Find E(X) and Var(X ) in terms of a and B using the MGF

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