- #1

endeavor

- 176

- 0

[itex]Pr(w,x,y,z) = Pr(w) Pr(z|y) Pr(y|x,w)Pr(x)[/itex]

show that x is independent of w by showing that Pr(x,w) = Pr(x)Pr(w).

Attempt: if we simply assume Pr(x,w) = Pr(x)Pr(w), then:

[itex]

\begin{align}

Pr(w,x,y,z) &= Pr(w) Pr(z|y) Pr(y|x,w) Pr(x)\\

&\stackrel{?}= Pr(x,w) Pr(z|y) Pr(y|x,w)\\

&\stackrel{?}= Pr(z|y) Pr(w,x,y)

\end{align}

[/itex]

But can we say the last line equals Pr(w,x,y,z)? I think this problem can be solved by simply applying Bayes' rule several times, but I can't seem to wrap my head around it.