
Bernoulli Distribution
< Probability Distributions List A Bernoulli distribution is a discrete probability distribution for a Bernoulli trial — a random experiment that has only two possible outcomes (usually called a “success” or a “failure”). The probability of success is P and the probability of failure is 1 – P. For example, the probability of getting a […]

Dummy variable
< Probability and statistics definitions A dummy variable is a numerical variable used in regression analysis to represent subgroups of the sample in your study. In research design, a dummy variable is often used to distinguish different treatment groups. In the simplest case, we would use a 0,1 dummy variable where a person is given […]

Linear Transformation
< Statistics and Probability Definitions A linear transformation is a special case of a vector transformation with two properties: addition must be preserved, and scalar multiplication must be preserved. How to check whether your transformation is linear. Addition must be Preserved: To check if addition is preserved, take two vectors u and v and add […]

Sampling theory
< Statistics and Probability Definitions In statistics, sampling theory is the body of principles underlying the drawing of samples that accurately represent the population from which they are taken. These methods are principally designed for large, inhomogeneous populations of discrete items, such as motor vehicles, books in libraries, or people. The primary objective of sampling […]

Joint probability distribution
< Probability distributions A joint probability distribution shows the likelihood of two events occurring together and at the same point in time. In other words, joint probability is the probability of event Y occurring at the same time that event X occurs. Joint probability is important because it allows statisticians to better understand the relationship […]

Sample in statistics
< Probability and statistics definitions A sample in statistics is small part of a larger population. The use of samples allows researchers to conduct their studies with more manageable data and in a timely manner. Generally speaking, the larger the sample size, the more accurate the results will be. This is because randomly drawn samples […]

Independent and identically distributed (i.i.d)
> Statistics and Probability Definitions In statistics, we commonly deal with random samples. A random sample can be thought of as a set of objects that are chosen randomly. Or, more formally, it’s “a sequence of independent and identically distributed (IID) random variables”. In other words, the terms random sample and IID are basically one […]

Sample mean: definition & Examples
< Statistics and probability definitions In statistics, the sample mean is an average of a set of data. This measure of central tendency can be used to calculate the standard deviation and variance of a data set. The sample mean can also be applied to determine population averages. Many industries employ the use of statistical […]

Independence of Events
< Statistics and Probability Definitions In probability theory and statistics, two events are independent if the occurrence of one event does not affect the chances of the occurrence of the other event. The mathematical formulation of the independence of events A and B is the probability of the occurrence of both A and B being […]

Degrees of Freedom
< Statistics and Probability Definitions When it comes to statistical data, the term “degrees of freedom” (df) refers to the maximum number of values that can be independently varied in a given sample. In other words, it’s a measure of how much freedom you have when selecting values for your data sample. But how do […]