Question $\mathbb{E}(X^2 +Y | Y =2) $
Whereas the answer is $\mathbb{E}(X^2|Y =2)+2$
Where did I go wrong? What would your approach be?
2026-04-22 01:26:11.1776821171
Expansion of conditional probability with $X$ and $Y$
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I do not see a difference of two squares here, and also how a factorization of $X^2 + Y$ could help here. On the other hand, every conditional expectation $\mathbf E[- \mid \mathfrak A]$ is linear. Hence $$ \def\E#1{\mathbf E\left[#1\right]} \E{X^2 + Y \mid Y = 2} = \E{X^2\mid Y = 2} + \E{Y \mid Y =2} = \E{X^2\mid Y = 2} + 2 $$ To discuss your solution here, you should write down your calculations.