There are Cauchy distributions in a two-class one-dimensional classification problem as follows:
$$P(x\mid w_i )=\frac{1}{πb}\frac{1}{1+((x-a_i)/b)^2}, i=1,2; a_2>a_1$$
I'm requested to plot $P(w_1 |x)$ and $P(w_2 |x)$ on one axis with $a_1=3, a_2=5$ and $b=1$. (Assuming $P(w_1) = P(w_2)$).
I know that $$P(w_1 | x)=(P(w_1 )P(x│w_1 ))/P(x) $$
But I can't get how I can plot $P(w_i|x)$, however I can plot $P(x|w_i)$ and I get the following pic:
Did I miss something, or just the plot is the answer?
I get this if in the function I introduce $P(x) = P(x|w_1) + P(x|w_2)$:
