The Conditional Expectation of Y Given X, E(Y $X = x )$

Multiple Choice

The conditional expectation of Y given X, E(Y $X = x )$ , is calculated as follows:

A) $\sum _ { i= 1 } ^ { k } Y _ { i } \operatorname { Pr } \left( X = x _ {i} \mid Y = y \right)$
B) E $[ E ( Y \mid X ) ] ]$
C) $\sum _ { i= 1 } ^ { k } y _ { l } \operatorname { Pr } \left( Y = y _ {i} \mid X = x \right)$
D) $\sum _ { i = 1 } ^ { k } E \left( Y \mid X = x _ { i } \right) \operatorname { Pr } \left( X = x _ { i } \right)$