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Let (X, Y) be a pair of Bivariate normal variables with means X, Y and variances 2 X, 2 Y respectively. Let be the correlation

Let (X, Y) be a pair of Bivariate normal variables with means X, Y and variances 2X, 2Y respectively. Let be the correlation between X and Y.

(a) For s, t R, compute E(esX+tY ).

(b) Compute E[(X + 2Y )3].

(c) Compute the conditional density of X given that X + Y = X + Y .

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