hypergeometric distribution

(noun)

a discrete probability distribution that describes the number of successes in a sequence of $n$ draws from a finite population without replacement

Related Terms

Examples of hypergeometric distribution in the following topics:

  • Hypergeometric Distribution

    • The hypergeometric distribution is used to calculate probabilities when sampling without replacement.
    • You can calculate this probability using the following formula based on the hypergeometric distribution:

  • The Hypergeometric Random Variable

    • The hypergeometric distribution is a discrete probability distribution that describes the probability of $k$ successes in $n$ draws without replacement from a finite population of size $N$ containing a maximum of $K$ successes.
    • The hypergeometric distribution applies to sampling without replacement from a finite population whose elements can be classified into two mutually exclusive categories like pass/fail, male/female or employed/unemployed.
    • The following conditions characterize the hypergeometric distribution:
    • A random variable follows the hypergeometric distribution if its probability mass function is given by:
    • A hypergeometric probability distribution is the outcome resulting from a hypergeometric experiment.

  • Practice 5: Hypergeometric Distribution

  • Notation for the Hypergeometric: H = Hypergeometric Probability Distribution Function X ~ H (r,b,n)

    • Read this as "X is a random variable with a hypergeometric distribution. " The parameters are r, b, and n. r = the size of the group of interest (first group), b = the size of the second group, n = the size of the chosen sample
    • NOTE : Currently, the TI-83+ and TI-84 do not have hypergeometric probability functions.

  • Student Learning Outcomes

  • Common Discrete Probability Distribution Functions

    • Some of the more common discrete probability functions are binomial, geometric, hypergeometric, and Poisson.
    • Most elementary courses do not cover the geometric, hypergeometric, and Poisson.
    • A probability distribution function is a pattern.
    • These distributions are tools to make solving probability problems easier.
    • Each distribution has its own special characteristics.

  • Hypergeometric (optional)

    • The outcomes of a hypergeometric experiment fit a hypergeometric probability distribution.
    • This is a hypergeometric problem because you are choosing your committee from two groups (men and women).

  • The Binomial Formula

    • The binomial distribution is a discrete probability distribution of the successes in a sequence of $n$ independent yes/no experiments.
    • This makes Table 1 an example of a binomial distribution.
    • In probability theory and statistics, the binomial distribution is the discrete probability distribution of the number of successes in a sequence of $n$ independent yes/no experiments, each of which yields success with probability $p$.
    • The binomial distribution is the basis for the popular binomial test of statistical significance.
    • If the sampling is carried out without replacement, the draws are not independent and so the resulting distribution is a hypergeometric distribution, not a binomial one.

  • How Fisher Used the Chi-Squared Test

    • Fisher's exact test is preferable to a chi-square test when sample sizes are small, or the data are very unequally distributed.
    • As pointed out by Fisher, under a null hypothesis of independence, this leads to a hypergeometric distribution of the numbers in the cells of the table.
    • However, the significance value it provides is only an approximation, because the sampling distribution of the test statistic that is calculated is only approximately equal to the theoretical chi-squared distribution.
    • The approximation is inadequate when sample sizes are small, or the data are very unequally distributed among the cells of the table, resulting in the cell counts predicted on the null hypothesis (the "expected values") being low.

  • For each problem:

    • Two distributions may be used to solve this problem.
    • Use one distribution to solve the problem.
    • Hint: Use the Hypergeometric distribution.
    • Solve the following questions (d-f) using that distribution.
    • Define the random variable X and give its distribution.