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I have a tutorial question which I am not sure what it means.

X1, X2 are continuous random variable. They are joint normal distribution with correlation $\rho$

Find the distribution of


My question is: Does it mean to find

$fa_1x_1,a_2x_2(x_1,x_2)$ ?

or does it mean to find

$f_Y(y<a_1x_1+a_2x_2)$ ?

I have tried to expand the later and it seems to be very tough.

Thank you!

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It seems that the latter is meant. The explicit calculations may be difficult, but you'd at least expect a normal distribution, won't you? What might the $\mu$ and $\sigma$ of the new distribution be? Warning! The variance is greatly influenced by the covariance. –  Hagen von Eitzen Sep 28 '12 at 6:13
Thank you I think I get it! –  K_R Sep 28 '12 at 6:21

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