Show that it is possible to have Xn -→ X in probability, but not to have P{Xn E (a, b)} – + P{X € (a, b)} for all intervals (a, b).

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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Show that it is possible to have Xn
→ X in probability, but not to have
P{Xn E (a, b)} → P{X € (a,b)} for all intervals (a, b).
Transcribed Image Text:Show that it is possible to have Xn → X in probability, but not to have P{Xn E (a, b)} → P{X € (a,b)} for all intervals (a, b).
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