Skip to main content

# Questions tagged [conditional-expectation]

For every question related to the concept of conditional expectation of a random variable with respect to a $\sigma$-algebra. It should be used with the tag (probability-theory) or (probability), and other ones if needed.

4,204 questions
Filter by
Sorted by
Tagged with
1 vote
0 answers
14 views

• 29
-2 votes
0 answers
37 views

0 votes
1 answer
36 views

• 406
0 votes
0 answers
35 views

### How to ensure that integrals are remain within limits of domain of the variables?

I have a Manager who has no information about the profit from investment into two bonds, other than the fact that they are independently drawn from uniform distribution ${m, 1}$ where, m>0. Profit ...
1 vote
1 answer
61 views

### What's the relationship between $(X_i)$ and $(X_i - \mathbb{E}[X_i | X_{<i}])$?

Let $X_1,\cdots,X_n$ be $n$ random variables on the same probability space $(\Omega, F, P)$, all with expectation $0$. Define $Y_i=X_i - \mathbb{E}[X_i | X_1, \cdots, X_{i-1}]$. Is it true that for ...
• 45
0 votes
1 answer
70 views

• 351
1 vote
0 answers
52 views

• 684
1 vote
0 answers
84 views

### Intuition why pulling out $\mathcal{G}$-measurable $X$ of $E[f(X,Y)|\mathcal{G}]$ requires $Y$ indep of $\mathcal{G}$

Given $\mathcal{G}$ a sigma-field and $X$ a $\mathcal{G}$-measurable random variable, on an intuitive level, why do we need $Y$ to be independent of $\mathcal{G}$ to pull out $X$ from the conditional ...
• 1,297
1 vote
1 answer
42 views

### Why do we need square integrability in showing $E(Y|X)$ minimizes expected quadratic loss?

I've read about that $E(Y|X)=\underset{f(x)\in \mathcal{F}}{\arg\min} E(Y-f(X))^2$, where $\mathcal{F}$ is the set of all square integrable functions in $x$. The proof of this result is simple and ...
• 503
0 votes
1 answer
27 views

### Bayesian updating on expectation with many candidates

I have an individual selected for a job. He was competing against 10 candidates. All individuals are independently drawn from uniform distribution U(0,1). Him being chosen means he is better than the ...
0 votes
1 answer
40 views