Question: A random variable X has the probability density function f (x) = 2(1 x), 0 < x < 1. (a) Find the moment generating

A random variable X has the probability density function f (x) = 2(1 − x), 0 < x < 1.

(a) Find the moment generating function for X.

(b) Use the moment generating function to find a formula for E(Xk).

(c) Let Y = 1 2 (X + 1). Find M[Y; t].

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