Let X be a random variable that follows the exponential distribution with a rate parameter1.(a) Compute P(X > 0.5[X > 0.3).(b) Show that the moment generating function of X is Mx(t) =iidExponential(1). Use moment generating func-(c) Suppose that you have X1,.., X30tions to show that Xi follows the Gamma distribution with shape parameter 30and rate parameter 1.Hint: You may use the following fact without proving it: the mgf of Gamma-distributionwith parameter a (shape) and 3 (rate) is (1 – )-a.(d) Let XP(X < 1.2)?2525 E Xi. How would you use the central limit theorem to approximatei3D1

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Answered: Let X be a random variable that follows…

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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