In probability theory, if a random variable X has a binomial distribution with parameters n and p, i.e., X is distributed as the number of "successes" in n independent Bernoulli trials with probability p of success on each trial, then Probability theory is the mathematical study of probability. ... A random variable can be thought of as the numeric result of operating a non-deterministic mechanism or performing a non-deterministic experiment to generate a random result. ... See binomial (disambiguation) for a list of other topics using that name. ... In the theory of probability and statistics, a Bernoulli trial is an experiment whose outcome is random and can be either of two possible outcomes, called success and failure. ...

for any x ∈ {0, 1, 2, ... n}. If np and n(1 − p) are large (sometimes taken to mean ≥ 5), then the probability above is fairly well approximated by

where Y is a normally distributed random variable with the same expected value and the same variance as X, i.e., E(Y) = np and var(Y) = np(1 − p). This addition of 1/2 to x (if x greater than mean) is a continuity correction. If x less than mean, it will be necessary a subtraction of 1/2. The normal distribution, also called Gaussian distribution, is an extremely important probability distribution in many fields, especially in physics and engineering. ... In probability theory (and especially gambling), the expected value (or mathematical expectation) of a random variable is the sum of the probability of each possible outcome of the experiment multiplied by its payoff (value). Thus, it represents the average amount one expects to win per bet if bets with identical... In probability theory and statistics, the variance of a random variable is a measure of its statistical dispersion, indicating how far from the expected value its values typically are. ...

A continuity correction can also be applied when other discrete distributions supported on the integers are approximated by the normal distribution. For example, if X has a Poisson distribution with expected value λ then the variance of X is also λ, and In probability theory and statistics, the Poisson distribution is a discrete probability distribution (discovered by Siméon-Denis Poisson (1781–1840) and published, together with his probability theory, in 1838 in his work Recherches sur la probabilité des jugements en matières criminelles et matière civile [Research on the...

if Y is normally distributed with expectation and variance both λ.

See also Yates' correction for continuity. Yates correction for continuity, or Yates chi-square test, adjusts the formula for Pearsons chi-square test by subtracting 0. ...