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Ppose A 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, ß) is defined by the following f(u) = Ba)y"(1 – y)*-1, 0 0, ß > 0, otherwise, { f(y) %3D 0, where B(a, ß) T(a)I"(3) T(a+ß) * (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 = x.

Ppose A 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, ß) is defined by the following f(u) = Ba)y"(1 – y)*-1, 0 0, ß > 0, otherwise, { f(y) %3D 0, where B(a, ß) T(a)I"(3) T(a+ß) * (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 = x.

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 X|Y ~ 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(@, B) is defined by the following { Bay"(1 – y)B-1, 0<y<1,a > 0, ß > 0, otherwise, f(y) 0, where B(a, B) r(a)I(8) 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 = x.
Transcribed Image Text:2. Let X and Y be two random variables. Suppose X|Y ~ 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(@, B) is defined by the following { Bay"(1 – y)B-1, 0<y<1,a > 0, ß > 0, otherwise, f(y) 0, where B(a, B) r(a)I(8) 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 = x.
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