Question I1.(a) Let the random variable X have a continuous distribution with the probabilitydensity 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 thatc= 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 FunctionMx(t), find the mean and the variance of X.(iv) Let a new random variable, Y, be such that X := Y® where p > 0. Findthe pdf of Y and clearly state its domain.

Answered: Image /qna-images/answer/c331257c-e619-475c-85bd-3572d4282980.jpg

Answered: (a) Let the random variable X have a…

Trigonometry (MindTap Course List)

10th Edition

ISBN:9781337278461

Author:Ron Larson

Publisher:Ron Larson

Chapter6: Topics In Analytic Geometry

Section6.4: Hyperbolas

Problem 5ECP: Repeat Example 5 when microphone A receives the sound 4 seconds before microphone B.

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