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Past exam of the mathematics course of the University of Cambridge / 2003 / iii / Paper 29 / 6 / a / Solution

Past exam of the mathematics course of the University of Cambridge / 2004 / iii / Paper 28 / 3 / c / Solution

Past exam of the mathematics course of the University of Cambridge / 2004 / iii / Paper 30 / 1 / c / Solution

Past exam of the mathematics course of the University of Cambridge / 2004 / iii / Paper 40 / 6 / iii / Solution

Past exam of the mathematics course of the University of Cambridge / 2004 / iii / Paper 41 / 4 / Solution

Past exam of the mathematics course of the University of Cambridge / 2004 / iii / Paper 7 / 3 / Solution

Past exam of the mathematics course of the University of Cambridge / 2004 / iii / Paper 7 / 4 / iii / Solution

Past exam of the mathematics course of the University of Cambridge / 2005 / iii / Paper 16 / 4 / a / Solution

Past exam of the mathematics course of the University of Cambridge / 2005 / iii / Paper 16 / 5 / i / Solution

Past exam of the mathematics course of the University of Cambridge / 2005 / iii / Paper 34 / 1 / a / ii / Solution

Past exam of the mathematics course of the University of Cambridge / 2005 / iii / Paper 34 / 1 / a / i / Solution

Past exam of the mathematics course of the University of Cambridge / 2005 / iii / Paper 34 / 1 / b / Solution

Past exam of the mathematics course of the University of Cambridge / 2005 / iii / Paper 34 / 2 / b / Solution

Past exam of the mathematics course of the University of Cambridge / 2005 / iii / Paper 38 / 2 / a / i / Solution

Past exam of the mathematics course of the University of Cambridge / 2005 / iii / Paper 48 / 4 / b / Solution

Past exam of the mathematics course of the University of Cambridge / 2005 / ii / Paper 2 / 28J / i / Solution

Past exam of the mathematics course of the University of Cambridge / 2006 / iii / Paper 14 / 1 / Solution

{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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