The conditional expectation of Y given $X , E ( Y \mid X = x )$
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) $\sum _ { i = 1 } ^ { k } y _ { i } \operatorname { Pr } \left( Y = y _ { i } \mid X = x \right)$
D) $\sum _ { i = 1 } ^ { l } E \left( Y \mid X = x _ { i } \right) \operatorname { Pr } \left( X = x _ { i } \right)$

Question

The conditional expectation of  Y  given $X , E ( Y \mid X = x )$
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) $\sum _ { i = 1 } ^ { k } y _ { i } \operatorname { Pr } \left( Y = y _ { i } \mid X = x \right)$
D) $\sum _ { i = 1 } ^ { l } E \left( Y \mid X = x _ { i } \right) \operatorname { Pr } \left( X = x _ { i } \right)$

Quizplus · Accepted Answer

The conditional expectation $E(Y \mid X = x)$ is calculated as $\sum y_i \operatorname{Pr}(Y = y_i \mid X = x)$, which is option C.

The Conditional Expectation of Y Given X,E(Y∣X=x)X , E ( Y \mid X = x )X,E(Y∣X=x)

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