Exercise 2 question (d) of homework 2

Exercise 2 question (d) of homework 2

by Gabin Paul Jacques Leroy -
Number of replies: 1

Hello,

I want to show that d_2(p(S)|| q(S))=D_{KL}( \tilde{p}|| \tilde{q}) where \tilde{p} and \tilde{q} are linked to p,q via some probability kernel W, in order to use the data processing inequality. Here is my reasoning : 

Data

Is this correct ? 

Best regards,

GL