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Let {Xn}-1 be a sequence of random variables that converges in probability n=1 Prove that the limiting random variable is unique P-a.s., i.e., if Xn 4 X and Xn 4 Y, then P(X = Y) = 1.

Let {Xn}-1 be a sequence of random variables that converges in probability n=1 Prove that the limiting random variable is unique P-a.s., i.e., if Xn 4 X and Xn 4 Y, then P(X = Y) = 1.

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter13: Probability And Calculus
Section13.CR: Chapter 13 Review
Problem 42CR
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Let {Xn}-1 be a sequence of random variables that converges in probability n=1 Prove that the limiting random variable is unique P-a.s., i.e., if Xn 4 X and Xn 4 Y, then P(X = Y) = 1.
Transcribed Image Text:Let {Xn}-1 be a sequence of random variables that converges in probability n=1 Prove that the limiting random variable is unique P-a.s., i.e., if Xn 4 X and Xn 4 Y, then P(X = Y) = 1.
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