Question: Two Gaussian random variables X and Y, with zero means and variances Ï 2 , between which there is a correlation coefficient p, have a

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).

x 2pxy+ y f(x, y) = exp 22 V1 -2 202 (1 p) exp (-y/ (2o)) fy (y) = V2?

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