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

Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter13: Probability And Calculus
Section13.2: Expected Value And Variance Of Continuous Random Variables
Problem 10E
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Suppose that Y₁ is a negative binomial random variable with p= .75 and r = 6, Y₂ is a
random variable with mean -5 and variance 11, and Y3 is a gamma random variable with
1.6 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
=
Transcribed Image Text:Suppose that Y₁ is a negative binomial random variable with p= .75 and r = 6, Y₂ is a random variable with mean -5 and variance 11, and Y3 is a gamma random variable with 1.6 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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ISBN:
9780321964038
Author:
GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:
Pearson Addison Wesley,