if x has a hypergeometric distribution with m = 3, n = 6, and n = 2, find the probability distribution of y, the number of successes minus the number of failures.
Answers
Hypergeometric Distribution
The probability distribution of a hypergeometric random variable is called a hypergeometric distribution. This lesson describes how hypergeometric random variables, hypergeometric experiments, hypergeometric probability, and the hypergeometric distribution are all related.
Notation
The following notation is helpful, when we talk about hypergeometric distributions and hypergeometric probability.
N: The number of items in the population.
k: The number of items in the population that are classified as successes.
n: The number of items in the sample.
x: The number of items in the sample that are classified as successes.
kCx: The number of combinations of k things, taken x at a time.
h(x; N, n, k): hypergeometric probability - the probability that an n-trial hypergeometric experiment results in exactly x successes, when the population consists of N items, k of which are classified as successes
Hypergeometric Experiments
A hypergeometric experiment is a statistical experiment that has the following properties:
A sample of size n is randomly selected without replacement from a population of N items.
In the population, k items can be classified as successes, and N - k items can be classified as failures.