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Past exam of the mathematics course of the University of Cambridge / 2008 / ia / Paper 2 / 9F / Solution

Past exam of the mathematics course of the University of Cambridge / 2008 / iii / Paper 34 / 3 / c / Solution

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Past exam of the mathematics course of the University of Cambridge / 2008 / iii / Paper 34 / 4 / c / Solution

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Past exam of the mathematics course of the University of Cambridge / 2008 / iii / Paper 39 / 2 / iii / Solution

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{title2=$\mathbb E[X\mid\mathcal G]$}
{wiki}

= Conditional expected value
{synonym}

= Conditional mean
{synonym}

For an integrable random variable $X$ and a sub-sigma-algebra $\mathcal G$, the conditional expectation $\mathbb E[X\mid\mathcal G]$ is the almost-everywhere unique $\mathcal G$-measurable integrable random variable satisfying
$$
\int_G\mathbb E[X\mid\mathcal G],d\mu=\int_GX,d\mu
$$
for every $G\in\mathcal G$.


Conditional expectation

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