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.
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.
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 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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F23cdc0d7-7d33-42d3-8fb9-b8ab1ea99c34%2F9e3b1759-2455-4f7b-8a84-244312159399%2Fzksg49h_processed.png&w=3840&q=75)
Transcribed Image Text:a. Let X be a continuous random variable which follows a Gamma distribution with
parameters 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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