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Suppose that the conditional distribution of Y given X = x is Poisson with mean E(Y|x) = x, and that X ~ exp(1)

Suppose that the conditional distribution of Y given X = x is Poisson with mean E(Y|x) = x, and that X ~ exp(1)

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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Could you solve (d),(e),(f)?

Thank you.

Suppose that the conditional distribution of Y given X = x is Poisson with mean A = E(Y|x) = x, and that X ~ exp(1) (a) Find fy (y) (b) Find E(Y) (c) Find Var(Y) (d) Find Var(E(Y|X) (e) Find E(Var(Y|X)) (f) Find f(x|y) (g) Find E(X|Y) (h) Find E(E(X|Y)) without using iterative expectation formula.
Transcribed Image Text:Suppose that the conditional distribution of Y given X = x is Poisson with mean A = E(Y|x) = x, and that X ~ exp(1) (a) Find fy (y) (b) Find E(Y) (c) Find Var(Y) (d) Find Var(E(Y|X) (e) Find E(Var(Y|X)) (f) Find f(x|y) (g) Find E(X|Y) (h) Find E(E(X|Y)) without using iterative expectation formula.
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