Problem 1Let (n,A,P) be a probability space. Show that the probability measureP is continuous from below, i.e. for any sequence of events A₁, A2,... EA with the property thatAn An+1 for all n EN, we haveHint: Define sets B₁, B2,... byP(Ů An) = lim P(A₂).n-∞n=1n-1Bn := An\UAk.k=1Show that BnBe=Ø whenever kl. Now express U-1 An in terms of the Bn, use the axiomsof the probability measure, and recall thatNΣP(B₁)= lim Σ P(B₂).N-00 n=1n=1

Problem 1 Let (n,A,P) be a probability space. Show that the probability measure P is continuous from below, i.e. for any sequence of events A₁, A2,... EA with the property that An An+1 for all n € N, we have Hint: Define sets B₁, B2,... by P(ŮA₂) = lim P(A₂). An n-x n=1 n-1 Bn:= An \UAk. k=1 Show that BnB = whenever k #l. Now express U-1 An in terms of the Bn, use the axioms of the probability measure, and recall that n=1 N EP ΣP(B) = lim Σ P(B₂). N-on=1 n=1

Problem 1 Let (n,A,P) be a probability space. Show that the probability measure P is continuous from below, i.e. for any sequence of events A₁, A2,... EA with the property that An An+1 for all n € N, we have Hint: Define sets B₁, B2,... by P(ŮA₂) = lim P(A₂). An n-x n=1 n-1 Bn:= An \UAk. k=1 Show that BnB = whenever k #l. Now express U-1 An in terms of the Bn, use the axioms of the probability measure, and recall that n=1 N EP ΣP(B) = lim Σ P(B₂). N-on=1 n=1

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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