PROBABILITY DISTRIBUTIONS

Let us begin with concept of random variable. It is a variable that takes different values with some probabilities. Suppose the random variable X under consideration refers to the possible outcomes (called events) of tossing a coin. There are two events in this case (Head and Tail), which are exhaustive and mutually exclusive, and have probability of occurrence 1/2 each. Similarly for
a fair dice there are six outcomes and each event has a probability of 1/6. We can generalize the concept as follows: A random variable X assumes values X₁, X₂,.......... X_n, with corresponding probabilities p₁, p₂, p₃,........ p_n,. We express it as p(X = X₁) = p₁. When the random variable assumes certain isolated values we call it a discrete random variable. On the other hand, if it assumes any value in an interval it is termed continuous random variable.

A probability distribution is a statement about the possible values of a random variable along with their respective probabilities. Thus it describes how the probabilities are distributed over the values of the random variable. For a discrete random variable the probability distribution function is called probability.mass function whereas for a continuous random variable it is
called probability density function.