Discrete Probability Distribution

For a discrete random variable, the probability mass function is given by p(X). where p_i is probability and X_i is a value of the random variable, The probability mass function should satisfy the following two conditions:

i) Probability of an event cannot be negative, i.e., for any value X_i, we have p(X_i) ≥ 0

ii) Probabilities of all possible outcomes sum to unity, i.e.,      Σ p(X_i) = 1

all x

There are quite a few discrete probability distributions. We present below the probability mass function of an important probability distribution, that is, binomial distribution.