Question: The probability density function of the beta distribution is given by x-(1-x)8-1 f(x)= = B(a, B) a > 0, 30, 0 < x

The probability density function of the beta distribution is given by x-(1-x)8-1 f(x)= = B(a, B) " a > 0, 30, 0 < x < 1. where, B(a, ) = x-1(1 - x)-1dx b) Show that EX" = == (a)(3) = T(a + B) B(a+n,3) T(a+n)T(a+B) B(a,B) T(a+B+n)(a)* EXERCISE 6 Show that 1. F(a+1) al(a). = 2. ()=.

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