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2. Let X and Y be two random variables. Suppose XY ~ Binomial (n, Y) where n is fixed and Y stands for the probability of success. Suppose the success probability Y is a random variable distributed as a Beta distribution, Y Beta(a, B). The PDF of Beta(a, B) is defined by the following { 0 < y < 1,a > 0, B>0, f(y) = 0, otherwise, where B(a, B) r(a)I(5) T(a+B)* (1) Find E(X|Y) and V(X|Y). (2) Find E(X). (3) Find Cor(X,Y). Hint: E(X|Y) is a linear function of Y. (4) Find the conditional PDF of Y given X = r. 3. Suppose X and Y

2. Let X and Y be two random variables. Suppose XY ~ Binomial (n, Y) where n is fixed and Y stands for the probability of success. Suppose the success probability Y is a random variable distributed as a Beta distribution, Y Beta(a, B). The PDF of Beta(a, B) is defined by the following { 0 < y < 1,a > 0, B>0, f(y) = 0, otherwise, where B(a, B) r(a)I(5) T(a+B)* (1) Find E(X|Y) and V(X|Y). (2) Find E(X). (3) Find Cor(X,Y). Hint: E(X|Y) is a linear function of Y. (4) Find the conditional PDF of Y given X = r. 3. Suppose X and Y

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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2. Let X and Y be two random variables. Suppose XY ~ Binomial (n, Y) where n is fixed and Y stands for the probability of success. Suppose the success probability Y is a random variable distributed as Beta(a, B). The PDF of Beta(a, B) is defined by the following a Beta distribution, Y f(u) = { Blaß)y'(1 – y)-1, 0 <y< 1,a > 0, ß > 0. ) < y < 1,a > 0,B > 0, 0, otherwise, where B(a, B) = T(@)I(ß) T(a+B)· (1) Find E(X|Y) and V(X|Y). (2) Find E(X). (3) Find Cor(X,Y). Hint: E(X|Y) is a linear function of Y. (4) Find the conditional PDF of Y given X r. 3. Suppose X and Y ero
Transcribed Image Text:2. Let X and Y be two random variables. Suppose XY ~ Binomial (n, Y) where n is fixed and Y stands for the probability of success. Suppose the success probability Y is a random variable distributed as Beta(a, B). The PDF of Beta(a, B) is defined by the following a Beta distribution, Y f(u) = { Blaß)y'(1 – y)-1, 0 <y< 1,a > 0, ß > 0. ) < y < 1,a > 0,B > 0, 0, otherwise, where B(a, B) = T(@)I(ß) T(a+B)· (1) Find E(X|Y) and V(X|Y). (2) Find E(X). (3) Find Cor(X,Y). Hint: E(X|Y) is a linear function of Y. (4) Find the conditional PDF of Y given X r. 3. Suppose X and Y ero
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