1. Suppose Y has a Bernoulli distribution with mean 1/4 and that the conditional distribution of X given Y has probability mass function fxy (s, t)=c₁(1-t)2 + c₂ts3, se {1,2...), te {0,1}, where C₁, C₂ > 0. (a) Find the values of the constant C₁, C2. (b) Find the joint probability mass function fx,y. (c) Find the moment generating function of X. (d) Are X and Y independent? Explain.
1. Suppose Y has a Bernoulli distribution with mean 1/4 and that the conditional distribution of X given Y has probability mass function fxy (s, t)=c₁(1-t)2 + c₂ts3, se {1,2...), te {0,1}, where C₁, C₂ > 0. (a) Find the values of the constant C₁, C2. (b) Find the joint probability mass function fx,y. (c) Find the moment generating function of X. (d) Are X and Y independent? Explain.
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.CR: Chapter 13 Review
Problem 29CR
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