Question: Let X be a continuous random variable with values in [0, 2] and density fX. Find the moment generating function g(t) for X if (a)

Let X be a continuous random variable with values in [0, 2] and density fX. Find the moment generating function g(t) for X if
(a) fX(x) = 1/2.
(b) fX(x) = (1/2)x.
(c) fX(x) = 1 − (1/2)x.
(d) fX(x) = |1 − x|.
(e) fX(x) = (3/8)x2.

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