5.20 As an alternative to the approach of Problem 5.19

(b) for calculating the moments of X ∼ B

(a, b), a general formula for EXk (similar to equation (5.43)) can be derived.

Do so, and use it to verify the mean and variance of X given in Problem 5.19. [Hint:

Write EXk as the integral of xc−1(1 − x)

d−1 and use the constant B

(c,

d) of Table 5.1.

Note that a similar approach will work for many other distributions, including the χ2, Student’s t, and F distributions.]