Question 1
Given a filtration $\mathcal{F}_t$, what does the conditional expectation $E[X|\mathcal{F}_t]$ represent in the context of financial modeling?
Question 2
Which of the following is a direct consequence of the projection property of conditional expectation?
Question 3
Consider a random variable $X$ and a sub-$\sigma$-algebra $\mathcal{G}$. If $X$ is independent of $\mathcal{G}$, what is $E[X|\mathcal{G}]$?
Question 4
Which of the following statements correctly defines conditional variance?
Question 5
In the context of filtering theory, what role does conditional expectation play?
