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Statistical classification is the problem of identifying the sub-population to which new observations belong, where the identity of the sub-population is unknown, on the basis of a training set of data containing observations whose sub-population is known. Therefore these classifications will show a variable behavior which can be studied by statistics.

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Bayes Optimal Classification Rule

Suppose that $Y∈ {0,1}$ and $P(Y=1) = 1/2$. The distribution of $X|Y= 0$ is discrete and is specified by $$P(X= 1|Y= 0) = 1/3 $$ $$P(X= 2|Y= 0) = 2/3$$The distribution of $X|Y= 1$ is discrete a …
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