# Bayes classifier of 2 classes

Given the prior probability of 2 distributions N(x,y) and N(a,b), where N(μ,σ^2):

how do you make a decision rule to minimize the probability of error, if the prior probabilities are equal? Can you give an example?

What if the prior probabilities are different, such as
P(Distribution 1) = 0.70
P(Distribution 2) = 0.30 ?

-
I have suggested some stylistic changes –  Henry Mar 11 '11 at 16:53
Though this is a very mathematical question, you might get a better response at stats.stackexchange.com –  Mitch Mar 11 '11 at 17:11

$$\text{classify} \ \textbf{x} \ \text{as} \ \begin{cases} C_{0} \ \ \ \ \text{if} \ P(C_0| \textbf{x}) > P(C_1| \textbf{x}) \\ C_1 \ \ \ \ \text{otherwise} \end{cases}$$