The successful study of probability distributions depends on your understanding of basic probability. You can use probability distributions to model different kinds of data sets and to identify significant patterns in my data.

A probability distribution describes the likelihood of the possible outcomes of a random event. Discrete probability distributions represent discrete random variables, or discrete events. Often, the outcomes of discrete events are expressed as whole numbers that can be counted.

Discrete and Continuous

The type of data that has clear spaces between values is discrete data. Discrete data is countable. There are distinct or different values in discrete data. Continuous information is information that falls into a continuous series. Continuous data is measurable. With continuous variables, you’re dealing with decimal values rather than whole numbers. For instance, all the decimals values between one and two, such as 1.1, 1.12, 1.125 and so on. Typically these are decimal values that can be measured such as height, weight, time or temperature.

For more information on discrete and continuous, check out the post called The Classification of Data.

Discrete Probability Distribution

Let’s consider an example of a discrete probability distribution. Consider the random event of a single die roll. The sample space for a single die roll is one, two, three, four, five and six. The term sample space is the set of all possible values for a random variable. The probability of each outcome for a fair die is the same. If you roll a die you have a sample space of {1, 2, 3, 4, 5, 6}. The probability of each outcome is one out of six or 16.7%. You can display a discreet probability distribution as a table or a graph. The distribution table summarizes the probability for each possible outcome.

Four common discrete probability distributions are

• Uniform
• Binomial
• Bernoulli
• Poisson

Poisson

The poisson distribution can model the number of customers in a given day.

The probability distribution for a continuous random variable can only tell you the probability that the variable takes on a range of values. Let’s check out an example to learn more. A continuous random variable may have an infinite number of possible values. Suppose you are measuring the height of students. Height is a continuous variable. The probability that a student is exactly and precisely 5 foot 9 is essentially zero. In this example you’ll need to use a continuous probability distribution to tell you the probability that the height of the student is in a certain range or interval. You are probably familiar with (or at lest heard of) of the bell curve, which refers to the graph for a continuous distribution called the normal distribution.