Question: (a) Show that M(t)M(t) is the moment generating function of X Y, where Y is independent of X but has the same distribution. (b)

(a) Show that M(t)M(−t) is the moment generating function of X − Y, where Y is independent of X but has the same distribution.

(b) In a similar way, describe random variables which have moment generating functions 1

2 − M(t )

, Z

∞

0 M(ut )e−u du.

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