48 Let , , 1, denote independent uniform (0, 1) random variables For 0 a 1, define TV by mm n Ul Un a (a) Show by induction that an P N n n (b) Prove that E N ea, and conclude that the expected number of random numbers needed until their sum exceeds 1 is equal to e ...

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*48. Let / , , /> 1, denote independent uniform (0, 1) random variables. For 0...

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*48. Let £ / , , /> 1, denote independent uniform (0, 1) random variables.

For 0 < a < 1, define TV by

Í = mm{n :Ul + · · · + Un> a]

(a) Show by induction that an P[N> n] = —

(b) Prove that E[N] = ea, and conclude that the expected number of random numbers needed until their sum exceeds 1 is equal to e.

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Introduction To Probability Models

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Authors: Sheldon M. Ross

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*48. Let / , , /> 1, denote independent uniform (0, 1) random variables. For 0...

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Introduction To Probability Models

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