Binomial Distribution

Binomial Probability Distribution

A probability distribution that summarizes the likelihood that a variable will take on one of two independent outcomes across a fixed number of trials.

Binomial Experiment

An experiment that has a fixed number of trials, mutually independent outcomes, and two possible outcomes, classified as success or failure.

Random Variable

A variable that takes on numerical values determined by the outcomes of a random experiment, such as counting successes in a binomial experiment.

Probability p

The likelihood of success on a single trial in a binomial experiment.

Variance

A measure of the dispersion of a set of values; in a binomial distribution, it is calculated as n * p * (1 - p).

Mean (µ) of Binomial Distribution

The expected value of a binomial random variable, calculated as n * p.

Cumulative Probability

The probability that a random variable takes on a value less than or equal to a certain number.

Binomial Formula

The formula used to calculate the probability of obtaining exactly k successes in n trials, given by p(X=k) = C(n, k) * p^k * (1-p)^(n-k).

C(n, k)

The number of combinations of n items taken k at a time, calculated as n! / (k!(n-k)!).

Expected Value

The average value or mean of a random variable, representing what you expect to happen in a given number of trials.