There are frequently situations where you have information on the conditional distribution of Y given X , but are interested in the conditional distribution of X given Y .
Recalling $\operatorname { Pr } ( Y = y \mid X = x ) = \frac { \operatorname { Pr } ( X = x , Y = y ) } { \operatorname { Pr } ( X = x ) }$
, derive a relationship between
$\operatorname { Pr } ( X = x \mid Y = y ) \text { and } \operatorname { Pr } ( Y = y \mid X = x )$
This is called Bayes' theorem.

Question

There are frequently situations where you have information on the conditional distribution of  Y  given  X , but are interested in the conditional distribution of  X  given  Y .
Recalling $\operatorname { Pr } ( Y = y \mid X = x ) = \frac { \operatorname { Pr } ( X = x , Y = y ) } { \operatorname { Pr } ( X = x ) }$
, derive a relationship between
$\operatorname { Pr } ( X = x \mid Y = y ) \text { and } \operatorname { Pr } ( Y = y \mid X = x )$
This is called Bayes' theorem.

Quizplus · Accepted Answer

The Answer of There are frequently situations where you have information on the conditional distribution of  Y  given  X , but are interested in the conditional distribution of  X  given  Y .
Recalling $\operatorname { Pr } ( Y = y \mid X = x ) = \frac { \operatorname { Pr } ( X = x , Y = y ) } { \operatorname { Pr } ( X = x ) }$
, derive a relationship between
$\operatorname { Pr } ( X = x \mid Y = y ) \text { and } \operatorname { Pr } ( Y = y \mid X = x )$
This is called Bayes' theorem.

There Are Frequently Situations Where You Have Information on the Conditional