For an integrable <random variable> $X$ and a sub-sigma-algebra $\mathcal G\subseteq\mathcal F$, the <conditional expectation> $Y=\mathbb E[X\mid\mathcal G]$ is an integrable, $\mathcal G$-measurable random variable satisfying
$$
\int_GY\,d\mathbb P=\int_GX\,d\mathbb P
$$
for every $G\in\mathcal G$.

Solution

Past exam of the mathematics course of the University of Cambridge / 2021 / iii / Paper 201 / 1 / a / Solution

 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2021/iii/paper-201/1/a/solution