b)A random variable X follows an exponential distribution, X~Exp(0), with parameter 0 > 0.Find the cumulative distribution function (CDF) of X.i)ii)Show that the moment generating function (MGF) of X is M(t)=iii)Use the MGF in (ii) to find the mean and variance of X.

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Answered: i) Find the cumulative distribution…

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter4: Eigenvalues And Eigenvectors

Section4.6: Applications And The Perron-frobenius Theorem

Problem 25EQ

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i) Find the cumulative distribution function (CDF) of X. 8 ii) Show that the moment generating function (MGF) of X is M(t) = 8-t iii) Use the MGF in (ii) to find the mean and variance of X. .