Two Gaussian random variables X and Y, with zero means and variances Ï 2 , between which

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Two Gaussian random variables X and Y, with zero means and variances Ïƒ², between which there is a correlation coefficient p, have a joint probability-density function given by

x² – 2pxy+ y f(x, y) = exp 2πσ2 V1 -ρ2 202 (1 – p²)

The marginal pdf of Y can be shown to be

exp (-y²/ (2o²)) fy (y) = V2ло?

Find the conditional pdf f_X|Y(X | Y).

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Principles of Communications Systems, Modulation and Noise

ISBN: 978-8126556793

7th edition

Authors: Rodger E. Ziemer, William H. Tranter

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Question Posted: Sep 19, 2018 01:09 PM

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Two Gaussian random variables X and Y, with zero means and variances Ï 2 , between which

Question:

x² – 2pxy+ y f(x, y) = exp 2πσ2 V1 -ρ2 202 (1 – p²) exp (-y²/ (2o²)) fy (y) = V2ло?

Step by Step Answer:

The conditional pdf f XY xy is given by Note that the conditional pdf of X given Y is Gaussian ...View the full answer

Principles of Communications Systems, Modulation and Noise

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