Answered: Proof Let X and Y be integrable random…

Proof Let X and Y be integrable random variables on the probability space (Ω,F,P)andA⊂Fbe a σ-field. Show that E[YE(X|A)] = E[XE(Y|A)], assuming that both integrals exist.

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter4: Vector Spaces

Section4.4: Spanning Sets And Linear Independence

Problem 68E: Proof Prove that if S1 is a nonempty subset of the finite set S2, and S1 is linearly dependent, then...

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Question

Proof

Let X and Y be integrable random variables on the probability space (Ω,F,P)andA⊂Fbe a σ-field. Show that E[YE(X|A)] = E[XE(Y|A)], assuming that both integrals exist.

With differentiation, one of the major concepts of calculus. Integration involves the calculation of an integral, which is useful to find many quantities such as areas, volumes, and displacement.

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