8. Demonstrate the following two properties of moment-generating functions, where X and Xi are discrete random variables,

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8. Demonstrate the following two properties of moment-generating functions, where X and Xi are discrete random variables, using the definition and properties of expectations:

(a) MaþbX ðtÞ ¼ eatMX ðbtÞ

(b) MTXi ðtÞ ¼

Q MXi ðtÞ if fXig are independent.

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