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Algebra & Trigonometry with Analytic Geometry

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section10.8: Probability

Problem 31E

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Question

Suppose X and Y are two independent and identically distributed geometric random
variables. The pmd of X is
P(X = x) = p(1 – p)*-1 for x = 1,2, ...
Show that P(X >x) = (1- p)-1.
Show that P(X 2r+T)|(X > T)] = P(X > x) where T is a positive integer, i.e.,
Find the moment-generating function of X.
Let Z = X +Y. What is the moment generating function of Z?

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