Categorical Distribution

By generalizing the Bernoulli distribution to $k$ states, we get a categorical distribution. The sample space is $\{s_1, s_2, \cdots, s_k\}$. The corresponding probabilities for each state are $\{p_1, p_2, \cdots, p_k\}$ with the constraint $\sum_{i=1}^k p_i = 1$.