The random variables (xi_{1}, xi_{2}, ldots, xi_{n}, ldots) are independent and uniformly distributed over ((0,1)). Let (v)

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The random variables \(\xi_{1}, \xi_{2}, \ldots, \xi_{n}, \ldots\) are independent and uniformly distributed over \((0,1)\). Let \(v\) be a random variable equal to the \(k\) for which the sum

\[ s_{k}=\xi_{1}+\xi_{2}+\ldots+\xi_{n} \]

exceeds 1 for the first time. Prove that \(M v=e\).

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Theory Of Probability

ISBN: 9781351408585

6th Edition

Authors: Boris V Gnedenko

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