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Probability and Statistics


Some Special Discrete Distributions

There are some specific distributions that come up in practice a lot, thus they have been given special names. Behind each of these special distributions there is a random experiment, so we study and understand these random experiments on which the random variable is defined, then we derive corresponding PMF/PDFPMF/PDF, and MGFMGF(when exists), then we can use this knowledge directly(without deriving) every time when these distributions comes in practice.

Discrete Uniform distribution:

Consider a random experiment of picking a number from 1,2,3,...,N1,2,3,...,N at random.

Let XX denote the number we picked. SX={1,2,...N}S_X=\{1,2,...N\}