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# If X and Y have a bivariate normal distribution with parameters mean1,mean2, variance1, variance2and P show...

If X and Y have a bivariate normal distribution with parameters mean1,mean2, variance1, variance2and P show that Z = aX + bY + c is N(a.mean1 + b.mean2 + c, variance1.variance2 + 2abp.variance1.variance2 + b^2.variance2, where a, b, and c are constants. Hint: Use the m.g.f. M(t1 t2) of X and Y to find the m.g.f. of Z.

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