Abstract: Let (X,θ), (X₁, θ₁), …, (X_n, θ_n) be R_d×{0, 1} valued independent identically distributed (iid) random variables (r. v.), with P (θ=1)=p₁ and P(θ=0)=p₀=1-p₁. Let the conditional density function of X given θ=i be f_i(x)dx, i=0, 1. (X₁, θ₁), …, (X_n, θ_n) are known samples called trainning samples usually. In practice we are asked to decide the value of θ based on the observation of X_i(i=l, 2,…,n)with the aid of these trainning samples.