Find a random variable X such that E[X^n ] = 1/(n+1) for all natural numbers n.

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Find a random variable X such that E[X^n ] = 1/(n+1) for all natural numbers n.

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Answer 1

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Consider the probability space $0,11, 3, X$ , where ${\cal B}$ is the Borel $\sigma$ -algebra on $0, 1$ and $\lambda$ the Lebesgue measure. Let $X$ be the random variable on $0,11, 3, X$ , defined by $X(z) = r$ . Then for any natural number $n$ we have

$n+11$

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Answer 2

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Find a random variable X such that E[X^n ] = 1/(n+1) for all natural numbers n.

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