Discussion Forum

Hello,

I would like to have precisions about the definition of probability kernel. First, we have one discrete random variable $X$ on a probability space $(\Omega,F,\Bbb{P})$ where we take the sigma field as the power set of $\Omega$. Let $D_X$ denotes the alphabet of $X$. Then we consider another alphabet, associated to another discrete random variable $Y$ on $(\Omega,F,\Bbb{P})$, that we call $D_Y$. So in the definition of the course, when it is written $W(y|x)$, it means $W(y|x)=\Bbb{P}( Y=y| X=x  )$ and this is defined since both $X$ and $Y$ are defined on the same probability space. Is my interpretation correct ?

Bests,

Gabin