Math Problem Solver

QUESTION 1 [12]

The bivariate beta type II pdf is defined by

fX1,X2

(x1, x2) = (24 (1 − x1 − x2)

−b)/

x

1−a

1 x

1−b

2

(1 − x1 − x2)

a+c

, x_1 > 0, x_2 > 0.

Find

(a) a, b and c; (2)

(b) E (X3

1X2

2

) ; and (5)

(c) the marginal pdf of X1.