Can I say that the random variables are independent by looking at the joint pdf and iff I can factor the two random variables from each other, say (X+1)(Y+2), they are independent?
If not, is there another way one can use to quickly determine based on the joint pdf that two RV's are independent?
Of do I always have to integrate out the other var to find the other marginal pdfs, multiply them together and see if they equal the joint?