# Concept derivation guides

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Concept guide



## [Finite conditional expectation: computing E[X|G] for a partition-generated σ-algebra, including a zero-mass block](/en/derivations/derivation-mko-conditional-expectation-01/?from=%2Fen%2Fderivations%2F%3Fq%3Dmko-conditional-expectation)

On Ω={0,1,2,3,4} with masses 1/8, 3/8, 1/4, 1/4, 0 and X taking the values 4, 0, 2, 6, 10 in order, let G be generated by the partition {0,1}, {2,3}, {4}. From the two defining conditions of conditional expectation (G-measurable, same integral on every event of G), find all versions of E[X|G]: prove they must equal 1 and 4 on the two positive-mass blocks and may take any value on the zero-mass block {4} (determined only almost surely), and explain why pointwise conditioning, checking only the total expectation, and the unweighted mean are all wrong.

Finite conditional expectation

derivation-mko-conditional-expectation-01





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