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## Main Question or Discussion Point

Hi, when asked to show that the addition of 2 independent RV's with the same distribution is once again of the same distribution, eg showing in gaussian that if X has mean m and variance v and Y has mean n and variance w then if i want to show that X + Y has gaussian distribution with mean m+n and variance w+v I use the product of their m.g.fs which is fine , when i get the result of this product, what is a good way to basically say that this shows the stability under additivity and that the parameters are m+n and w+v ?

Thanks

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