What is a discrete probability distribution?

The definition of the word `distribution’ refers to how something is shared out in a group or how it is spread out over an area. Let X be a random variable – a variable whose possible values are the outcomes of a random event. If X is a discrete random variable then its possible values belong to a discrete set of outcomes. If there are three possible outcomes then

$X\in\left\lbrace x_1,x_2,x_3\right\rbrace$.

The Uniform Probability Distribution

The uniform probability distribution describes a discrete distribution whereby each outcome has an equal probability. Consider a single dice roll. The set of possible outcomes is {1,2,3,4,5,6} – this is discrete. Each of these outcomes has a probability of 1/6 and therefore represents a discrete uniform distribution.

The Binomial Probability Distribution

The binomial probability distribution gives the probabilities for the outcomes where a number of trials are considered. Each trial has a probability of success or failure. For example, the number of times a head comes up when a coin is tossed repeatedly is a binomial random variable. For example, if the coin is tossed 10 times, the number of heads is restricted to integers between 0 and 10 inclusively and is a binomial random variable. Here we are considering the toss of a head to be a success and the number of trials is the number of coin tosses. Each of the outcomes has a different probability.