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(8) The moment generating function of the random variable X having the probability density function f(x) = (;) x²e¬*,-o < x < ∞ is:

(8) The moment generating function of the random variable X having the probability density function f(x) = (;) x²e¬*,-o < x < ∞ is:

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
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(8) The moment generating function of the random variable X having the probability density function f(x) = x²e-*,-o << x < o is: 1 1 (a) for It| <1 (b) for |t| < 1 (1-t)3 (1-t)2 1 (c) s for |t| <1 (d) for |t| <1 (1-t)5 (1-t)4
Transcribed Image Text:(8) The moment generating function of the random variable X having the probability density function f(x) = x²e-*,-o << x < o is: 1 1 (a) for It| <1 (b) for |t| < 1 (1-t)3 (1-t)2 1 (c) s for |t| <1 (d) for |t| <1 (1-t)5 (1-t)4
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Step 1

Since , the probability density function is given by , 

f(x)=\frac{1}{2}x^2e^{-x};-\infty <x<\infty

Our aim is to find the moment generating function.

 

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