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Math Help - how to...add 2 independent r.v. with gamma distribution

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    how to...add 2 independent r.v. with gamma distribution

    Let X and Y be independent variables. X~gamma(alpha1,beta) and Y~gamma(alpha2,beta)....how do you show X+Y~gamma(alpha1+alpha2,beta) I know since var are independent you can break them apart? so alpha1+ alpha2 but what about beta+beta ...how is this equal to just beta?are is this the wrong calculation? thanks
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    Quote Originally Posted by pastadee View Post
    Let X and Y be independent variables. X~gamma(alpha1,beta) and Y~gamma(alpha2,beta)....how do you show X+Y~gamma(alpha1+alpha2,beta) I know since var are independent you can break them apart? so alpha1+ alpha2 but what about beta+beta ...how is this equal to just beta?are is this the wrong calculation? thanks
    Use a moment generating function approach.
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