Solution

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

Past exam of the mathematics course of the University of Cambridge / 2006 / iii / Paper 35 / 1 / d / Solution

Past exam of the mathematics course of the University of Cambridge / 2006 / iii / Paper 35 / 6 / Solution

Past exam of the mathematics course of the University of Cambridge / 2006 / iii / Paper 39 / 3 / Solution

Past exam of the mathematics course of the University of Cambridge / 2006 / iii / Paper 39 / 4 / Solution

Past exam of the mathematics course of the University of Cambridge / 2006 / iii / Paper 41 / 5 / c / Solution

Past exam of the mathematics course of the University of Cambridge / 2006 / iii / Paper 43 / 4 / Solution

Past exam of the mathematics course of the University of Cambridge / 2006 / iii / Paper 45 / 4 / g / Solution

Past exam of the mathematics course of the University of Cambridge / 2006 / iii / Paper 47 / 6 / b / Solution

Past exam of the mathematics course of the University of Cambridge / 2007 / ib / Paper 1 / 18C / ii / Solution

Past exam of the mathematics course of the University of Cambridge / 2007 / iii / Paper 32 / 3 / Solution

Past exam of the mathematics course of the University of Cambridge / 2007 / iii / Paper 33 / 1 / a / Solution

Past exam of the mathematics course of the University of Cambridge / 2007 / iii / Paper 33 / 1 / c / ii / Solution

Past exam of the mathematics course of the University of Cambridge / 2007 / iii / Paper 33 / 1 / c / i / Solution

Past exam of the mathematics course of the University of Cambridge / 2007 / iii / Paper 36 / 1 / a / Solution

Past exam of the mathematics course of the University of Cambridge / 2007 / iii / Paper 37 / 4 / Solution

Past exam of the mathematics course of the University of Cambridge / 2007 / iii / Paper 38 / 1 / Solution

Past exam of the mathematics course of the University of Cambridge / 2007 / iii / Paper 45 / 4 / 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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