24. Let X have the Pareto pdf f(x; k, )


k x

k

1 k

 x 

0 x 

introduced in Exercise 10.

a. If k 1, compute E(X).

b. What can you say about E(X) if k
1?

c. If k 2, show that V(X)
k 2

(k  1)2

(k  2)1

.

d. If k
2, what can you say about V(X)?

e. What conditions on k are necessary to ensure that E(Xn

)

is finite?