Answer to Question #107606 in Statistics and Probability for Website is good

Question

What criteria are required when using the following distributions? Give a clear example of each
- Uniform
- Binomial
- Hypergeometric

Answer 1

A uniform distribution, sometimes also known as a rectangular distribution, is a distribution that has constant probability.

The uniform distribution is used under these conditions:

minimum is fixed.

maximum is fixed.

all values in range are equally likely to occur.

discrete uniform is the discrete equivalent of the uniform distribution.

The requirements for a random experiment to be a binomial experiment are:

a fixed number (n) of trials

each trial must be independent of the others

each trial has just two possible outcomes, called “success” (the outcome of interest) and “failure“

there is a constant probability (p) of success for each trial, the complement of which is the probability (1 – p) of failure, sometimes denoted as q = (1 – p)

The hypergeometric distribution is used under these conditions:

total number of items (population) is fixed.

sample size (number of trials) is a portion of the population. A sample of size n is randomly selected without replaccement  from a population of N items, wherein each draw is either a success or a failure.

probability of success changes after each trial.