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4. A random vector 22m _ k(y+1) 039331 and Oy1+$ fT($' y) _ { 0 otherwise has the joint p.d.f. fT(a:, y) given by (a)

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4. A random vector 22m _ k(y+1) 039331 and Oy1+$ fT($' y) _ { 0 otherwise has the joint p.d.f. fT(a:, y) given by (a) Sketch the region of the 513,}; plane on which fT(:1:, y) is positive. (b) Find the value of k: which makes fT(:c, y) a probability density function. (0) Calculate the probability that X + Y 3 1

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