SOME DISCRETE DISTRIBUTIONS
In this chapter we present some frequently used discrete distributions.
3.1 DISCRETE UNIFORM, BINOMIAL AND BERNOULLI DISTRIBUTIONS
Definition 3.1 (Discrete Uniform Distribution) A random variable X has a discrete uniform distribution with N points, where N is a positive integer with possible distinct values xi, i = 1,2, · · · , N, if its probability mass function is given by:
If in particular xi = i, i = 1,2, · · · , N, the probability mass function is shown in Figure 3.1.
Theorem 3.1 (Properties of a Discrete Uniform Random Variable)If X is a random variable having a discrete uniform distribution with N points, then:
Corollary 3.1 If xk = k, k = 1,2, · · · , N, then:
- Left as an exercise for the reader.
- Follows from the definition of the mgf. ...