For > 0, > 0, and > 0, the following function is called
Chapter , Problem 28(choose chapter or problem)
For > 0, > 0, and > 0, the following function is called the bivariate Dirichlet probability density function f (x, y) = 0( + + ) 0()0()0( ) x1 y1 (1 x y) 1 if x 0, y 0, and x + y 1; f (x, y) = 0, otherwise. Prove that fX, the marginal probability density function of X, is beta with parameters (, + );and fY is beta with the parameters (, + ).Hint: Note that0( + + )0()0()0( ) =8 0( + + )0()0( + )98 0( + )0()0( )9= 1B(, + )1B(, ).
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