Probability Distribution > The Muth distribution, a model for non-negative continuous random variables, was introduced by Muth in 1977 [1]. The distribution has largely been overlooked in the statistical literature [2]; the distribution isn’t usually encountered in introductory probability and…

## Multivariate Distribution: Definition

Probability Distributions > Multivariate distributions show comparisons between two or more measurements and the relationships among them. For each univariate distribution with one random variable, there is a more general multivariate distribution. For example, the normal distribution is univariate and…

## Bivariate Distribution

Probability Distributions > A bivariate distribution (or bivariate probability distribution) is a joint distribution with two variables of interest. The bivariate distribution gives probabilities for simultaneous outcomes of the two random variables. A discrete joint distribution has at most a…

## Benford Distribution: Definition, Examples

Probability Distributions > Benford’s law , which concerns the spread of leading significant digits, states that the first (non-zero) digit in a wide range of number collections isn’t uniform for the number 1 through 9. Instead, the numbers follow the…

## Modified Geometric Distribution

Probability Distributions > The modified geometric distribution gives the number of failures until the first success in a series of independent trials. The modified geometric distribution starts at zero—that’s why it’s sometimes called the zero-modified (or zero-truncated) geometric distribution; a…

## Bernoulli Trials: Definition, Examples

Bernoulli Distribution > What are Bernoulli Trials? A Bernoulli trial is an experiment with two possible outcomes: Success or Failure. “Success” in one of these trials means that you’re getting the result you’re measuring. For example: If you flip a…

## Experimental Probability Examples in Real Life

Probability in Real Life > Experimental probability is the results from an actual experiment of repeated trials. In class, examples are sometimes given with coin tosses or dice rolling. For example, you could toss a coin 50 times to see…

## Tree Diagram Real Life Example

Probability in Real Life > A probability tree diagram is one way to study the sample space of an experiment. They are often helpful for studying outcomes and probabilities for multistage experiments. Any situation where an “experiment” is multistage can…

## Application of Hypergeometric Distribution in Real Life

Probability in Real Life > The hypergeometric distribution describes the number of successes in a sequence of n trials from a finite population without replacement. At first glance, it might seem that this is a purely academic distribution, but there…

## Subjective Probability Examples in Real Life

Subjective Probability Examples in Real Life In real life, we have to act, choose, decide, guess, and judge on imperfect information [1]. It’s this imperfect information that leads us to use subjective probability to make decisions. As it’s basically an…