csci5521/assignments/hwk01/HW1.md

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1. (20 points) \c{Derive the VC dimension of the following classifiers.}

3. (20 points) \c{Let P (x|C) denote a Bernoulli density function for a class $C \in {C_1, C_2}$ and P (C) denote the prior}

   a. \c{Given the priors P (C_1) and P (C_2), and the Bernoulli densities specified by p_1 \equiv p(x = 0|C_1) and p_2 \equiv p(x = 0|C_2), derive the classification rules for classifying a sample x into C_1 and C_2 based on the posteriors P (C_1|x) and P (C_2|x). (Hint: give rules for classifying x = 0 and x = 1.)}

   For $x=0$, the posteriors $P(C_i | x)$ are given by $P(C_i | x = 0) = \frac{p(x = 0 | C_i) p(C_i)}{p(x = 0)}$.
   
   - $p(x = 0 | C_i)$ is given to us as $p_1$