List the four requirements for a binomial distribution Descr

List the four requirements for a binomial distribution. Describe an experiment which is binomial and discuss how the experiment fits each of the four requirements.

Solution

The binomial distribution describes the behavior of a count variable X if the following conditions apply:

1: The number of observations n is fixed.

2: Each observation is independent.

3: Each observation represents one of two outcomes (\"success\" or \"failure\").

4: The probability of \"success\" p is the same for each outcome.

If these conditions are met, then X has binomial distribution with parameters n and p.

Example:

A fair six-sided die is rolled ten times, and the number of 6\'s is recorded.

There are fixed number of trials (ten rolls), each roll is independent of the others, there are only two outcomes (either it\'s a 6 or it isn\'t), and the probability of rolling a 6 is constant.