Suppose that Y₁ is a negative binomial random variable with p= .75 and r = 6, Y₂ is arandom variable with mean -5 and variance 11, and Y3 is a gamma random variable with1.6 and a = 5.9. Further suppose that all of these random variables are independent.(a) What is E[2Y₁ − 6Y2 + 5Y₁Y3]?(b) What is the variance of 3Y₁ +5Y2 - 8Y3?(c) What is the mgf of 7Y₁ +4Y3?0=

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A First Course in Probability (10th Edition)

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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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(a) What is E[2Y₁ - 6Y2 + 5Y₁Y3]? (b) What is the variance of 3Y₁ +5Y2-8Y3? (c) What is the mgf of 7Y₁ +4Y3?