There Are Frequently Situations Where You Have Information on the Conditional

Question

Examlex · Accepted Answer

The Answer is Given Pr(Y = y

\mid X

= x)=

\frac { \operatorname { Pr } ( X = x \mid Y = y ) } { \operatorname { Pr } ( X = x ) }

,
Pr(Y = y

\mid X

= x)× Pr(X = x)= Pr(X = x, Y = y);
similarly Pr(X = x

\mid Y

= y)=

\frac { \operatorname { Pr } ( X = x \mid Y = y ) } { \operatorname { Pr } ( X = x ) }

and
Pr(X = x

\mid Y

= y)× Pr(Y = y)= Pr(X = x, Y = y). Equating the two and solving for Pr(X = x

\mid Y

= y)then results in
Pr(X = x

\mid Y

= y)=

\frac { \operatorname { Pr } ( Y = y \mid X = x ) imes \operatorname { Pr } ( X = x ) } { \operatorname { Pr } ( Y = y ) }

.

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