X~Gamma(theta,alpha)
y~Gamma(theta,beta)
U=X/Y
V=X+Y
Find fX,Y(x,y)
State whether U and V are independent
Find marginal pdf
i am having trouble finding fX,Y(x,y) using information given that X and Y are of Gamma distribution.
And what is the theorem used to determine the independence of U and V?
hmm im having problem with the gamma distribution in this question
fx,y(X,Y) = {[(theta)^(alpha+beta)][x^(alpha-1)][y^(beta-1)][e^(-theta*(x+y))]}/[T(alpha+beta)] ??
or is it
fx,y(X,Y) = {[(theta)^(alpha+beta)][x^(alpha-1)][y^(beta-1)][e^(-theta*(x+y))]}/[T(alpha)T(beta)] ??
or am i completely wrong? help~
(T is that sign thats like a an upside down mirrored L)
What you need is here: Gamma distribution - Wikipedia, the free encyclopedia. Multiply the pdf's of X and Y together.