# Tag Info

Accepted

### Expectation of $X$ conditional on $aX+(1-a)Y>c$.

I don't know if you are looking for a closed and simplified solution based on the values of $a$ and $c$, but one approach for any problems in the conditional expectation is as follows: As you have ...
• 620
Accepted

### Calculating $E[X^2|X+Y]$ for $X,Y\sim N(0,1)$ independent

Actually $E(X^{2}|X+Y)=\frac 1 4(X+Y)^{2}+\frac 1 2$ if $X,Y$ is i.i.d. $N(0,1)$. To see this note that $E(X^{2}|X+Y)=E(Y^{2}|X+Y)$ since the joint distribution of $(X,Y)$ does not change when you ...
• 6,029
Accepted

### Conditional expectation with multiple random variables

It's the total law of probability: take the partition $\{C_1,C_2\}$ then $$\mathbb{E}[N_7|T] = \sum_{i=1}^{2} \mathbb{E}[N_7|T \cap C_i] \mathbb{P}[C_1|T]$$
• 724