While proving $E\left[E\left[X|Y\right]\right]=E[X]$ I saw use of this $$\sum_yP\left(Y=y|X=x\right)=1$$ but can't comprehend why is it so, please explain? I saw this on wikipedia page here
2026-04-07 03:18:15.1775531895
Why $\sum_yPr\left(Y=y|X=x\right)=1$?
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Since $$\sum_yP\left(Y=y|X=x\right)=1\Longleftrightarrow\sum_yP\left(Y=y\wedge X=x\right)=P(X=x)$$