Let X and Y be integrable random variables on the probability space (Ω,F,P)andA be a sub-σ-field of F. Show that (i) if X ≤ Y a.s., then E(X|A) ≤ E(Y|A) a.s.;
Let X and Y be integrable random variables on the probability space (Ω,F,P)andA be a sub-σ-field of F. Show that (i) if X ≤ Y a.s., then E(X|A) ≤ E(Y|A) a.s.;
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.8: Probability
Problem 36E
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i)
Let X and Y be integrable random variables on the probability space (Ω,F,P)andA be a sub-σ-field of F. Show that (i) if X ≤ Y a.s., then E(X|A) ≤ E(Y|A) a.s.; (ii) if a and b are constants, then E(aX + bY|A)=aE(X|A)+bE(X|A)
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