Let X Gamma (a, p), Y~ Gamma (a, 6), so 1 BAIT (41) + fx (x...
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Let X Gamma (a₁, p), Y~ Gamma (a₂, 6), so 1 BAIT (41) +² fx (x | a₁, p) = x>0 1 fr(y | a₂, B) = Bª²T (₂) 4²²-¹e²%, y>0 (az) Assuming they are independent. Let U = XY, V = X+Y. (a) What is the joint pdf of (U, V)? (b) Are U and V independent? Why? (c) What are the marginal distributions of U and V? Let X Gamma (a₁, p), Y~ Gamma (a₂, 6), so 1 BAIT (41) +² fx (x | a₁, p) = x>0 1 fr(y | a₂, B) = Bª²T (₂) 4²²-¹e²%, y>0 (az) Assuming they are independent. Let U = XY, V = X+Y. (a) What is the joint pdf of (U, V)? (b) Are U and V independent? Why? (c) What are the marginal distributions of U and V?
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To find the joint pdf of U V we need to use the transformation method Let u XY and v X Y Then we can ... View the full answer
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