#2,Suppose that X and Y have joint density given by:f (x, y) = 15x²y,0 < x < y < 1.(a) Find the marginal pdf of Y.(b) Find the conditional pdf of X given Y.(c) Find the conditional expectation of X given Y = 1/3.(d) Are X andY independent? Show this in two different ways.(e) Give an integral expression for P(X + 2Y < 1), but do not evaluate it.

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Answered: Suppose that X and Y have joint density…

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter7: Distance And Approximation

Section7.3: Least Squares Approximation

Problem 32EQ

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Suppose that X and Y have joint density given by: f (x, y) = 15x²y, 0 < x < y < 1. (a) Find the marginal pdf of Y. (b) Find the conditional pdf of X given Y. (c) Find the conditional expectation of X given Y = 1/3.