I have two normal populations S1 and S2, where S1 ~ N (μ1, σ1) and S2 ~ N (μ2, σ2) respectively. The populations are independent of each other and a data point X has to be either from S1 or from S2. Suppose that I have been given the estimates of μ1, μ2, σ1, σ2 and I’ve been given the priori probability of S1 and S2, say P(S1) = π1 and P(S2) = π2.
My question is, given a data point X1, how do I classify the data X1 into S1 or S2 with the given information. The data I have in not labelled so I cannot go for supervised learning.
I have tried to solve using simple Bayesian probability, but since, X1=x is a real values number not an interval, my numerator will logically be zero.
How should I solve this? I'm stuck. Can anyone show me some direction?