Hypergeometric Distribution

Hypergeometric distribution

A discrete probability distribution characterized by a fixed number of dependent trials, n, and a specified number of countable successes, x.

Dependent trials

Trials where the outcome of one affects the probability of the outcome of another, such as choosing without replacement.

Fixed number of successes

The total number of possible successes in the entire population, denoted by k.

Hypergeometric random variable

Denoted by capital X, it counts the number of successes in n dependent trials.

Mean of hypergeometric distribution

Calculated using the formula mu = n * (k / N), where N is the population size.

Variance of hypergeometric distribution

Calculated using the formula σ² = [n * k * (N - k) * (N - n)] / [N² * (N - 1)].

Probability of obtaining x successes in n trials

Given by P(X = x) = [C(k,x) * C(N-k, n-x)] / C(N,n), where C represents the combination function.

Rounding rule for probabilities

When calculating probabilities for hypergeometric distributions, round to four decimal places.

Comparison of distributions

The hypergeometric, binomial, and Poisson distributions; hypergeometric and binomial involve fixed trials, while the Poisson does not; binomial and Poisson involve independent trials, while hypergeometric involves dependent trials.