Question 3 [10 marks]. Suppose that X, Y and Z are statistically independent random variables, each of them with a x²(2) distribution. (a) Find the moment generating function of U = X + 3Y + Z. State clearly and justify all steps taken. (b) Calculate the expectation E(U) using the moment generating function.
Question 3 [10 marks]. Suppose that X, Y and Z are statistically independent random variables, each of them with a x²(2) distribution. (a) Find the moment generating function of U = X + 3Y + Z. State clearly and justify all steps taken. (b) Calculate the expectation E(U) using the moment generating function.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.8: Probability
Problem 22E
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![Question 3 [10 marks]. Suppose that X, Y and Z are statistically independent
random variables, each of them with a x²(2) distribution.
(a) Find the moment generating function of U = X + 3Y + Z. State clearly and
justify all steps taken.
(b) Calculate the expectation E(U) using the moment generating function.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F06c09651-aae3-40a2-ab82-7de7754ef13e%2F4922e339-959a-4046-a9ff-9cc6b5484d8d%2F7nr2sgi_processed.png&w=3840&q=75)
Transcribed Image Text:Question 3 [10 marks]. Suppose that X, Y and Z are statistically independent
random variables, each of them with a x²(2) distribution.
(a) Find the moment generating function of U = X + 3Y + Z. State clearly and
justify all steps taken.
(b) Calculate the expectation E(U) using the moment generating function.
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