Let X₁ and X₂ be two independent random variables with normal distributions N(1,9) and N(-3,16), respectively. Find the moment generating function of Y= X₁ + X₂. What distribution is associated with this moment generating function?
Let X₁ and X₂ be two independent random variables with normal distributions N(1,9) and N(-3,16), respectively. Find the moment generating function of Y= X₁ + X₂. What distribution is associated with this 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 24E
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![Let X₁ and X₂ be two independent random variables with normal distributions N (1,9) and
N(-3,16), respectively. Find the moment generating function of Y= X₁ + X₂. What
distribution is associated with this moment generating function?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe3a652e0-a9a3-4849-af75-fe64da18d594%2F8ea362ad-f351-4e0d-bc5b-8d9ddc19d1b7%2Ffreadjc_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Let X₁ and X₂ be two independent random variables with normal distributions N (1,9) and
N(-3,16), respectively. Find the moment generating function of Y= X₁ + X₂. What
distribution is associated with this moment generating function?
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