Use Theorem 5.9 to show that for the Poisson distribution α₃ = 1/√λ, where α₃ is the measure of skewness defined in Exercise 4.26. Theorem 5.9: The moment-generating function of the Poisson distribution is given by MX(t) = e^(λ(et – 1))
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The MGF of the Poisson distribution is given by: MX(t) = e^(λ(e^t - 1)) To find the nth moment, we take the nth derivative of the MGF with respect to t and then evaluate it at t = 0. First moment (n = 1): M'X(t) = d/dt [e^(λ(e^t - 1))] = λe^t * e^(λ(e^t - Show more…
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