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7.25. Let X₁, X2, ... be a sequence of independent and identically distributed continuous random variables. Let N≥ 2 be such that X₁ ≥ X₂ ≥ ≥ XN-1 < XN That is, N is the point at which the sequence stops decreasing. Show that E[N] = e.

7.25. Let X₁, X2, ... be a sequence of independent and identically distributed continuous random variables. Let N≥ 2 be such that X₁ ≥ X₂ ≥ ≥ XN-1 < XN That is, N is the point at which the sequence stops decreasing. Show that E[N] = e.

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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7.25. Let X₁, X2, ... be a sequence of independent and identically distributed continuous random variables. Let N 2 be such that X₁ ≥ X₂ ≥ … ≥ XN-1 < XN That is, N is the point at which the sequence stops decreasing. Show that E[N] = e. Hint: First find P{N ≥n}.
Transcribed Image Text:7.25. Let X₁, X2, ... be a sequence of independent and identically distributed continuous random variables. Let N 2 be such that X₁ ≥ X₂ ≥ … ≥ XN-1 < XN That is, N is the point at which the sequence stops decreasing. Show that E[N] = e. Hint: First find P{N ≥n}.
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