If X and Y have a bivariate normal distribution with joint probability density fXY (x, y X, Y, X, Y, p), show that the marginal probability distribution of X is normal with mean X and standard deviation X Hint Complete the square in the exponent and use the fact that the integral of a normal probability density function for a single variable is 1

Question: If X and Y have a bivariate normal distribution with joint probability density fXY (x, y; X, Y, X, Y, p), show that the marginal

If X and Y have a bivariate normal distribution with joint probability density fXY (x, y; σX, σY, μX, μY, p), show that the marginal probability distribution of X is normal with mean μX and standard deviation σX. [Hint: Complete the square in the exponent and use the fact that the integral of a normal probability density function for a single variable is 1.]

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