There Are Frequently Situations Where You Have Information on the Conditional

question 50

Essay

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.

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