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Show that N+ is continuous in probability, i.e. for any arbitrarily small € > 0, P{|N₁ − Ns| > ε } → 0, as s→ t. Hint. Use the stationary increments property (N₂ - N₁ ~ Nts if s≤t) and notice that Nu > ε is the same as Nu > 0 for small ε. (Why?)

Show that N+ is continuous in probability, i.e. for any arbitrarily small € > 0, P{|N₁ − Ns| > ε } → 0, as s→ t. Hint. Use the stationary increments property (N₂ - N₁ ~ Nts if s≤t) and notice that Nu > ε is the same as Nu > 0 for small ε. (Why?)

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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Please help solve this question.  A hint to use within the work is provided. This is an ungraded lecture question that I would love to know how to do!

Show that N is continuous in probability, i.e. for any arbitrarily small € > 0, P{|Nt — Ns| > ɛ} → 0, as s → t. Hint. Use the stationary increments property (№ — N3 ~ №−s if s≤ t) and notice that N > ε is the same as Nu > 0 for small ε. (Why?)
Transcribed Image Text:Show that N is continuous in probability, i.e. for any arbitrarily small € > 0, P{|Nt — Ns| > ɛ} → 0, as s → t. Hint. Use the stationary increments property (№ — N3 ~ №−s if s≤ t) and notice that N > ε is the same as Nu > 0 for small ε. (Why?)
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