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(a) Let the random variable X have a continuous distribution with the probability density function (pdf) сехp(-аг) (т > 0) fx(x) = elsewhere, with a, c > 0. (i) State the conditions that need to be satisfied by the pdf and show that c = a. (ii) Compute a formula for the Moment Generating Function of X, Mx(t), and state its domain of validity. (iii) Using the method of differentiation for the Moment Generating Function Mx(t), find the mean and the variance of X. (iv) Let a new random variable, Y, be such that X := Y" where p > 0. Find the pdf of Y and clearly state its domain.

(a) Let the random variable X have a continuous distribution with the probability density function (pdf) сехp(-аг) (т > 0) fx(x) = elsewhere, with a, c > 0. (i) State the conditions that need to be satisfied by the pdf and show that c = a. (ii) Compute a formula for the Moment Generating Function of X, Mx(t), and state its domain of validity. (iii) Using the method of differentiation for the Moment Generating Function Mx(t), find the mean and the variance of X. (iv) Let a new random variable, Y, be such that X := Y" where p > 0. Find the pdf of Y and clearly state its domain.

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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part c and D

Question I1. (a) Let the random variable X have a continuous distribution with the probability density function (pdf) cexp(-ar) (r > 0) fx(x) = elsewhere, with a, c > 0. (i) State the conditions that need to be satisfied by the pdf and show that c= a. (ii) Compute a formula for the Moment Generating Function of X, Mx(t), and state its domain of validity. (iii) Using the method of differentiation for the Moment Generating Function Mx(t), find the mean and the variance of X. (iv) Let a new random variable, Y, be such that X := Y® where p > 0. Find the pdf of Y and clearly state its domain.
Transcribed Image Text:Question I1. (a) Let the random variable X have a continuous distribution with the probability density function (pdf) cexp(-ar) (r > 0) fx(x) = elsewhere, with a, c > 0. (i) State the conditions that need to be satisfied by the pdf and show that c= a. (ii) Compute a formula for the Moment Generating Function of X, Mx(t), and state its domain of validity. (iii) Using the method of differentiation for the Moment Generating Function Mx(t), find the mean and the variance of X. (iv) Let a new random variable, Y, be such that X := Y® where p > 0. Find the pdf of Y and clearly state its domain.
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