A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN: 9780134753119
Author: Sheldon Ross
Publisher: PEARSON
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How can I solve this question 7.25?

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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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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