We wish to design an anti-spam filter based on the frequency (number of occurrences) of the word "subscribe" in the e-mail body. Anti-spam filter computes a "score" which is assigned to each incoming e-mail, based on the frequency of keyword "subscribe" contained in the body message. Define a linear model for the probability density functions (Ωₛₚₐₘ|) and (Ωₘₐᵢₗ|) of the classes "spam" and "mail".
Find the Bayesian decision rule and compute the probability of error for the two cases of priors P(ωₘₐᵢₗ)=10P(ωₛₚₐₘ)
