a) Find the moment generating function of X~ Bernoulli(p).b) Find the moment generating function of S~ Binomial(n, p).c) Another useful fact about moment generating functions is the following:Theorem: Suppose (Xn)n>1 is a sequence of random variables with corresponding momentgenerating functions Mx, and X is a random variable with moment generating functionMx such that for some > 0 we have Mx (1) <∞ for all / € (-6, 6). Iffor all t,lim Mx, (t) = Mx (1)72-00then lim,→∞ Fx₂(x) = Fx(r) for all r where Fx is continuous. That is, if the momentgenerating functions of X₁ converge to the moment generating function of X, then thedistribution of X₁ converges to the distribution of X.Binomial(n,A), then the distribution of S₁, converges toUse this to show that if SnPoisson(X) as n→∞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 of X~ Bernoulli(p). LE CO