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For pe (0, 1), let X - Geom(p), i.e. P(X=n) =(1-p)"-¹p for n € N₁. Show that EX=. Hint: Use the fact that tx-1=x and interchange summation and differ- entiation.

For pe (0, 1), let X - Geom(p), i.e. P(X=n) =(1-p)"-¹p for n € N₁. Show that EX=. Hint: Use the fact that tx-1=x and interchange summation and differ- entiation.

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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Problem 2 For p € (0,1), let X - Geom(p), i.e. P{X=n} = (1-p)"-1p for n € N₁. Show that EX=. Hint: Use the fact that tx-¹=x and interchange summation and differ- entiation.
Transcribed Image Text:Problem 2 For p € (0,1), let X - Geom(p), i.e. P{X=n} = (1-p)"-1p for n € N₁. Show that EX=. Hint: Use the fact that tx-¹=x and interchange summation and differ- entiation.
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