(a)(b)Let X have a gamma distribution with parameters a = 2 and 0.Find the mode of X. Recall that the mode of a continuous randomvariable is the value where the pdf is the highest.If the mode is two, find P(X < 9.488). Tables are allowed for thisproblem only if sufficient justification is provided.(c)Find the fifth moment of X without the use of the moment gen-erating function. Simplify completely.

Given that X has gamma distribution with parameters .The PDF of X is given as:

Answered: Let X have a gamma distribution with…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

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Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Let X have a gamma distribution with parameters a = 2 and 0. Find the mode of X. Recall that the mode of a continuous random variable is the value where the pdf is the highest.