Let X have the Pareto
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) = kθ2(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?
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Chapter 4 Solutions
Probability and Statistics for Engineering and the Sciences
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