# Equation of the boundary between two classes

I have a question about one task: I have two classes w1 and w2 and we are working with 2D space. The density of each of the two classes are the folowing: $$$$p(x = {(x_{1}, x_{2})}'| w_{1}) = \frac{1}{4}\cdot e ^{-\frac{x_{1}+ x_{2}}{2}}$$$$ $$$$p(x = {(x_{1}, x_{2})}'| w_{2}) = \frac{1}{16}\cdot x_{1}x_{2} \cdot e ^{-\frac{x_{1}+ x_{2}}{2}}$$$$ How to find the equation of the boundary between the two classes.

• For finding a Bayes decision boundary, you need the priors of these classes. Are they equally likely? – gunes Apr 28 '20 at 15:23
• Yes, I think they are equally likely. – Stats8901 Apr 28 '20 at 15:46

If they're equally likely, you'll just solve $$p(x|w_1)=p(x|w_2)$$ to find the decision boundary, which yields the curve $$x_1x_2=4$$.
• $$x_1x_2=4p(w_1)/p(w_2)$$ – gunes Apr 28 '20 at 16:27