Discrete probability - Probability and probability Distributions, CSIR-NET Mathematical Sciences | Mathematics for IIT JAM, GATE, CSIR NET, UGC NET PDF Download

All probability distributions can be classified as discrete probability distributions or as continuous probability distributions, depending on whether they define probabilities associated with discrete variables or continuous variables.

Discrete vs. Continuous Variables

If a variable can take on any value between two specified values, it is called a continuous variable; otherwise, it is called a discrete variable.

Some examples will clarify the difference between discrete and continuous variables.

• Suppose the fire department mandates that all fire fighters must weigh between 150 and 250 pounds. The weight of a fire fighter would be an example of a continuous variable; since a fire fighter's weight could take on any value between 150 and 250 pounds.

• Suppose we flip a coin and count the number of heads. The number of heads could be any integer value between 0 and plus infinity. However, it could not be any number between 0 and plus infinity. We could not, for example, get 2.5 heads. Therefore, the number of heads must be a discrete variable.

Just like variables, probability distributions can be classified as discrete or continuous.

Discrete Probability Distributions

If a random variable is a discrete variable, its probability distribution is called a discrete probability distribution.

An example will make this clear. Suppose you flip a coin two times. This simple statistical experiment can have four possible outcomes: HH, HT, TH, and TT. Now, let the random variable X represent the number of Heads that result from this experiment. The random variable X can only take on the values 0, 1, or 2, so it is a discrete random variable.

The probability distribution for this statistical experiment appears below.

The above table represents a discrete probability distribution because it relates each value of a discrete random variable with its probability of occurrence. On this website, we will cover the following discrete probability distributions.

• Binomial probability distribution

• Hypergeometric probability distribution

• Multinomial probability distribution

• Negative binomial distribution

• Poisson probability distribution

Note: With a discrete probability distribution, each possible value of the discrete random variable can be associated with a non-zero probability. Thus, a discrete probability distribution can always be presented in tabular form.