Let y1 and y2 be independent random variables with


Let Y1 and Y2 be independent random variables with moment-generating functions MY1 (t) and MY2 (t), respectively. If a1 and a2 are constants, and U = a1Y1 + a2Y2 show that the moment-generating function for U is MU = MY1 (t) × MY2 (t).

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Basic Statistics: Let y1 and y2 be independent random variables with
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