The conditional distribution of Y given $X = x , \operatorname { Pr } ( Y = y \mid X = x )$
is
A) $\frac { \operatorname { Pr } ( Y = y ) } { \operatorname { Pr } ( X = x ) }$
B) $\sum _ { i = 1 } ^ { l } \operatorname { Pr } \left( X = x _ { i } , Y = y \right)$
C) $\frac { \operatorname { Pr } ( X = x , Y = y ) } { \operatorname { Pr } ( Y = y ) }$
D) $\frac { \operatorname { Pr } ( X = x , Y = y ) } { \operatorname { Pr } ( X = x ) }$

Question

The conditional distribution of  Y  given $X = x , \operatorname { Pr } ( Y = y \mid X = x )$
is
A) $\frac { \operatorname { Pr } ( Y = y ) } { \operatorname { Pr } ( X = x ) }$
B) $\sum _ { i = 1 } ^ { l } \operatorname { Pr } \left( X = x _ { i } , Y = y \right)$
C) $\frac { \operatorname { Pr } ( X = x , Y = y ) } { \operatorname { Pr } ( Y = y ) }$
D) $\frac { \operatorname { Pr } ( X = x , Y = y ) } { \operatorname { Pr } ( X = x ) }$

Quizplus · Accepted Answer

The conditional probability $\operatorname{Pr}(Y = y \mid X = x)$ is defined as the joint probability $\operatorname{Pr}(X = x, Y = y)$ divided by the marginal probability $\operatorname{Pr}(X = x)$.

The Conditional Distribution of Y Given X=x,Pr⁡(Y=y∣X=x)X = x , \operatorname { Pr } ( Y = y \mid X = x )X=x,Pr(Y=y∣X=x)

The Conditional Distribution of Y Given $X = x , \operatorname { Pr } ( Y = y \mid X = x )$