Problem in STATISTICAL INFERENCE. Need solution (preferably step by step) for pr

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Problem in STATISTICAL INFERENCE.

Need solution (preferably step by step) for problem (a), picture is below or can be found here: http://i64.tinypic.com/2ee8ny8.png

PROBLEM 1.9. We consider two independent gamma distributed variables, X Gamma (a, 1) and Y Gamma (B, 1). Define U X Y and V (X +Y) a Find the simultaneous density fu,v. Verify that UN Gamma (a B, 1) indep. of V. b) Explain that V is beta (a,B) distributed with normalisation constant B B). c) Comment that Ba, 3) 1 for a B 1 and therefore T +B) T(a)T (3) d) Find the distribution of (1 S/T) 1 when S amma (a,Y) indep. of T n Gamma (B, n)

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