Let x and y have a bivariate normal distribution and suppose that x and y both have

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Let x and y have a bivariate normal distribution and suppose that x and y both have mean 0 and variance 1, so that their marginal distributions arc standard normal and their joint density is

-1 p(x, y) = {2 (1- p)] ' exp{- (x 2pxy + y)/(1 p)}. .

Show that if the correlation coefficient between x and y is p, then that between x² and y² is p².

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Bayesian Statistics An Introduction

ISBN: 9781118332573

4th Edition

Authors: Peter M. Lee

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Question Posted: Nov 28, 2023 02:53 AM

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Let x and y have a bivariate normal distribution and suppose that x and y both have

Question:

p(x, y) = {2π √(1-p²)}" ¹ exp{-1 (x² − 2pxy + y²)/(1 − p²)}. .

Step by Step Answer:

The correlation coefficient between two random variables is given by the formula P...View the full answer

Bayesian Statistics An Introduction

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