Key Concepts in Probability Distributions

Binomial experiment

An experiment with 4 conditions: fixed number of trials, only two outcomes (success/failure), same chance of success each time, and trials are independent.

Binomial probability distribution

A chart or list showing the chances of getting a certain number of successes in a binomial experiment.

Binomial probability function

The formula used to calculate binomial probabilities.

Bivariate probability distribution

A distribution that gives the chances for combinations of outcomes involving two variables.

Continuous random variable

A variable that can take any value within a range (like height or time).

Discrete random variable

A variable that can only take certain values (like 0, 1, 2, ...).

Discrete uniform probability distribution

A distribution where all outcomes are equally likely.

Empirical discrete distribution

A distribution based on actual data, using observed frequencies to estimate probabilities.

Expected value

The average outcome you'd expect from many trials of an experiment.

Hypergeometric probability distribution

A distribution showing the chance of getting a certain number of successes when choosing from a group without replacement.

Hypergeometric probability function

The formula used to find probabilities in a hypergeometric situation.

Poisson probability distribution

A distribution showing the chance of a certain number of events happening in a fixed time or space.

Poisson probability function

The formula used to calculate Poisson probabilities.

Probability distribution

A way to show how likely each outcome of a random variable is.

Probability function

A function that gives the probability of each value for a discrete random variable.

Random variable

A number that represents the outcome of a random experiment.

Standard deviation

A measure of how spread out the values of a variable are, based on the square root of variance.

Variance

A measure of how much the values of a variable vary from the average.