Question: Let X be a nonnegative integer valued random variable with a pdf fx (x) satisfying the relation fx (a) = 4fx (2 - 1) x

Let X be a nonnegative integer valued random variable with a pdf fx (x) satisfying the relation fx (a) = 4fx (2 - 1) x = 1, 2, 3, ... (a) Explicitly evaluate the pdf f. (b) Factorial Moment Generating Function (FMGF) is defined by Mx (t) = E(tx ). The FMGF generates factorial moments of X via My"(1) = E[(X),], where (X)n =X(X - 1) . .. (X -n + 1). Derive the FMGF for X and based on that evaluate E[X(X - 1)(X - 2)]

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