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Please give step-by-step instructions for solving these.

Let X ~ Exp(Beta).

(a) Find E(X^(-1/2)).
(b) Find an expression for E(X^k), where k is a positive integer.
(c) Use part (b) to show that V(X) = 1 / (Beta^2).

Where
X = Exponential Distribution
E(X) = Expected Value
V(X) = Variance

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Solution Summary

Positive integers are emphasized within these problems. Steps are thoroughly given to guide users.

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