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stukbv
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Homework Statement
I need to show that if X ~ r(a1,B) Y ~ r(a2,b) where r means gamma distribution then if X and Y are independent
i) X+Y ~ r(a1+a2,B)
ii) cX ~ r(a1,cB)
Homework Equations
The Attempt at a Solution
i) i use the mgfs of x and y and ended up with mgf(x+y) = (1/1-Bt)^(a1 + a2 )
I am told this is enough to prove i, is this correct or what could i say to make it better?
ii) i am a bit stuck on this one, i mean, would you just put c in front of all the x's in the pdf and then re-derive the mgf? or is there something extra?
thanks