The factorial moment-generating function for any random variable W is the expected value of tw. Moreover dr/dtr E(tW)|t=1 = E[W(W ˆ’ 1)・・・(W ˆ’ r + 1)]. Find the factorial moment-generating function for a geometric random variable and use it to verify the expected value and variance formulas given in Theorem 4.4.1.

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E(X) Var(X)=4