Prove that Y1 and Y2 are independent

mahalekrishna · April 2nd, 2009, 10:12 pm

QuoteOriginally posted by: PdISince the event{X₁+X₂=y₁,X₁/(X1+X2)=y₂}is equivalent with the event{X₂=y₁(1-y&#8322,X₁=y₂y₁}we obtain for the densityf(y1,y2)=exp(-y1*(1-y2))*exp(-y1*y2) =exp(-y1)yikes.. you transformed the space (plane) without accounting for the jacobian

PdI · April 3rd, 2009, 9:13 am

You right, the Jacobian is abs(det[y2 y1;1-y2 -y1 ])=y1 so you get f(y1,y2)=y1*exp(-y1)