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)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
icon
Related questions
Question
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.
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.
Expert Solution
steps

Step by step

Solved in 3 steps with 3 images

Blurred answer
Similar questions
Recommended textbooks for you
A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
Probability
ISBN:
9780134753119
Author:
Sheldon Ross
Publisher:
PEARSON
A First Course in Probability
A First Course in Probability
Probability
ISBN:
9780321794772
Author:
Sheldon Ross
Publisher:
PEARSON