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

1. ## 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

2. Originally Posted by pastadee
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.