Conditional probability

JesperHP

TS Contributor
#1
I am consideriing the following identities:

\(p(s' \lvert s,a) = p(x'_1,x'_2,c' \lvert x_1,x_2,c,a_1,a_2) = \pi(c'\lvert c)p(x'_2 \lvert x_2,c,a_2)p(x'_1 \lvert x_1,c,a_1)\)

My problem is that \(x'_1 =f( x_1,c,a_1)\) and \(x'_2 =f( x_2,c,a_2)\) are deterministic functions. So I am guessing these measures \(p(x'_2 \lvert x_2,c,a_2)p(x'_1 \lvert x_1,c,a_1)\) must both be degenrate. I what to keep x_1' as deterministic but I want to put a measure on a_2 and make x'_2 random. But how can I convincingly write this?