Fordiscreterandomvariables X and Y , derivethefollowinggeneralizationofBayes’Theorem

(Section 2.1.5):

P(X = x S Y = y) = P(Y = y S X = x)P(X = x)

Σa P(Y = y S X = a)P(X =

a) , where thedenominatorsumisover allthepossiblevalues a for X. Statethecorresponding result for P(Bj S A) for anevent A and asamplespacethatpartitionsintodisjointevents

{B1, ...,Bc}.