What does it mean to say that the real-valued RVs X and Y are inde- pendent, and how, in terms of the joint PDF fyy could you recognise whether X and Y are independent? The non-negative RVs X and Y have the joint PDF Sx.y (x, y) =;(x+y)e-(&+»)/(x, y > 0), x, y e R. Find the PDF fx and hence deduce that X and Y are not independent. Find the joint PDF of (1X, tY), where i is a positive real number. Suppose now that T is an RV independent of X and Y with PDF if 0

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