If i have the mgf of X and the mgf of Y where X~N(mx,vx) and Y~N(my,vy) and X and Y are independent ,(adsbygoogle = window.adsbygoogle || []).push({});

then if i want to show that aX +bY ~ N(amx+bmy , a^2vx+b^2vy) how would i do this - need to be able to do the convolutions way and the mgf's way,

for the mgfs way is it just, mgf(ax+by) = mgf(ax) . mgf(bx) if so how do you find mgf(ax) ?

Thanks

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# Stability of the gaussian under addition and scalar multiplication

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