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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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a sequence of random variables X1, X2, . ... Suppose X, follows a discrete distri-
bution taking two possible values {0, n²}, with P(X, = 0) = 1 – 1 and P(X, = n²) = !.
Calculate E(X„). What happens to E(X) as n → ∞?
Does X, converge in probability to some real number? If so, find that number
and prove. If not, explain.

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