70. Let X~ Xn.(a) 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 =(c) Use the mgf for X to derive the formula for the variance of X,o² = V(X) = E(X²) - [E(X)]² = m (0) - [m'x (0)]².E(X) = m'x (0).

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Answered: (a) Find the moment generating function…

A First Course in Probability (10th Edition)

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(a) 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). u (c) Use the mgf for X to derive the formula for the variance of X, o² = V(X) = E(X²) - [E(X)]² = m (0) - [mx (0)]².