Question: Let X be a positive random variable; i.e., P(X 0) = 0. Argue that (a) E(1/X) 1/E(X) (b) E[log X] log[E(X)] (c) E[log(1/X)]
Let X be a positive random variable; i.e., P(X ≤ 0) = 0. Argue that
(a) E(1/X) ≥ 1/E(X)
(b) E[−log X]≥ −log[E(X)]
(c) E[log(1/X)] ≥ log[1/E(X)]
(d) E[X3] ≥ [E(X)]3.
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a E1X 1EX The first part of this is to show that the expectation of a ratio is greater than that of its first term The second part is to show that the expected value of a random variable X is greater ... View full answer
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