# Probability Distribution - Explained

What is a Probability Distribution?

# What is a Probability Distribution?

A probability distribution is a mathematical and statistical theory that describes the likelihood of the occurrence of the possible values of a random variable. A probability distribution assigns or plots the possible values of a variable based on the likelihood of their occurrence and whether the occurrence is minimum or maximum. To plot possible values using probability distribution, there are some critical factors that must be considered such as standard deviation, average, normal distribution, bell curve, and others. There are normal distributions used in obtaining the likely occurrence of the possible values that a random variable can take or assume. The normal distribution or bell curve is the most commonly used. Before a probability distribution can be done, the statistician or mathematician must be versed with the random variables available, all the possible outcomes each of the random variables can assume as well as the probability of the outcomes occurring. Also, generating data for probability distribution determines where a possible value should be plotted.

Back to: RESEARCH, ANALYSIS, & DECISION SCIENCE

## How is a Probability Distribution Used?

The major types of probability distributions are;

• Normal distribution: The normal distribution is the most basic form of distribution that occurs naturally in scenarios. It is otherwise called the bell curve, it is a continuous probability distribution that occurs in statistics and used in natural situations. The normal distribution occurs when the possible outcomes or distributions of random variables are not known.
• Chi-square distribution: This type of probability distribution is used when comparing two independent variables. Chi-square distribution refers to the distribution of a sum of squares of independent standard normal random variables.
• Poisson distribution: The Poisson distribution is a type of distribution that determines the possibility of a number of outcomes occurring during a fixed space of time given that the events or random variables occur independently of the previous event. The Poisson distribution was developed by Simeon Denis Poisson, a French mathematician.
• Binomial distribution: Just like the Poisson distribution, the Binomial distribution is also a discrete probability distribution. This distribution expresses the possibility of an outcome of random variables or independent events using a polar question pattern or through a yes/no question.

Of all the forms of distribution, the normal distribution is the most used as it occurs in engineering, finance, statistics, science and investing.

## Probability Distributions Used in Investing

A critical field where probability distributions are mostly used is in the investment space. Given that investment can have either a positive or negative return, investors often seek to precisely predict the outcome of a given investment in order to know what investment position to take. Despite that, it is a wide held belief the stock returns and investment returns take the form of the normal distribution, investors and market analysts maintain that are expressed in kurtosis to a large extent. Risk managers also pay attention to probability distribution so as to know the likely amount of losses and gains associated with an investment portfolio.