a. Let X be a continuous random variable which follows a Gamma distribution withparameters a and B for r > 0.(i) Prove that the rth moment of X can be expressed as E(X") =Br I'(a+r)T(a)where r> 1.(ii) Using the result in (i), derive the variance of the random variable X.

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Answered: a. Let X be a continuous random…

A First Course in Probability (10th Edition)

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a. Let X be a continuous random variable which follows a Gamma distribution with parameters a and ß for r > 0. (i) Prove that the rh moment of X can be expressed as E(X") = Br r(a+r) T(a) where r > 1. (ii) Using the result in (i), derive the variance of the random variable X.