Cumulative Distribution Function

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We first try to understand what is the Conditional Cumulative Distribution Function.

Start from this function $F_{Y|X}(y|x)$, the definition is:

$$F_{Y|X}(y|x)=P(Y\le y|X=x)$$

Use human language, it means: Given that we know the value of $X$ is $x$, what is the probability that $Y$ is less than or equal to $y$?

You can also refer to the Conditional Expectation Function