How would I find the joint pdf of Y1 and Y2, where Y1 = X1 and Y2 is X1+X2+...+Xn, where the Xi's belong to gamma (1, theta)?
This would be a simple exercise is Y2 was X1+X2 or X1+X2+X3, but I don't know how to easily approach this when it is a sum of N random variables.
Thanks!