69. Let X~ Geom (p) with pmf f(x) = P(X = x) = p(1 − p)ª−¹I{1,2,...} (x).(a) Use the definition of the moment generating function of a discrete random variable to find the momentgenerating function mx (t) for X.(b) Use the mgf for X to derive the formula for the mean of X, μ = E(X) = m'x (0).

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Answered: (a) Use the definition of the moment…

A First Course in Probability (10th Edition)

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(a) Use the definition of the moment generating function of a discrete random variable to find the moment generating function mx (t) for X. (b) Use the mgf for X to derive the formula for the mean of X, µ = = E(X) = m'x (0).