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Past exam of the mathematics course of the University of Cambridge / 2009 / iii / Paper 101 / 3 / a / Solution

Past exam of the mathematics course of the University of Cambridge / 2009 / iii / Paper 101 / 3 / b / Solution

Past exam of the mathematics course of the University of Cambridge / 2009 / iii / Paper 31 / 1 / Solution

Past exam of the mathematics course of the University of Cambridge / 2009 / iii / Paper 31 / 5 / Solution

Past exam of the mathematics course of the University of Cambridge / 2009 / iii / Paper 32 / 5 / Solution

Past exam of the mathematics course of the University of Cambridge / 2009 / iii / Paper 33 / 4 / Solution

Past exam of the mathematics course of the University of Cambridge / 2009 / iii / Paper 39 / 4 / i / Solution

Past exam of the mathematics course of the University of Cambridge / 2009 / iii / Paper 40 / 6 / d / Solution

Past exam of the mathematics course of the University of Cambridge / 2009 / ii / Paper 1 / 28I / iii / Solution

Past exam of the mathematics course of the University of Cambridge / 2009 / ii / Paper 4 / 25J / Solution

Past exam of the mathematics course of the University of Cambridge / 2010 / iii / Paper 12 / 2 / i / Solution

Past exam of the mathematics course of the University of Cambridge / 2010 / iii / Paper 33 / 2 / Solution

Past exam of the mathematics course of the University of Cambridge / 2010 / iii / Paper 33 / 4 / Solution

Past exam of the mathematics course of the University of Cambridge / 2010 / iii / Paper 33 / 6 / Solution

Past exam of the mathematics course of the University of Cambridge / 2010 / iii / Paper 39 / 1 / b / Solution

Past exam of the mathematics course of the University of Cambridge / 2010 / iii / Paper 39 / 2 / a / Solution

Past exam of the mathematics course of the University of Cambridge / 2010 / iii / Paper 39 / 2 / c / 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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