Probability and Statistics

3

Special Distribution

3.1 Introduction

An experiment often consists of repeated ­trials, each with two possible outcomes—success or failure. For example, in a manufacturing industry, a test or trial may indicate a defective or non-defective item. We may choose to call either outcome as a success. This process is called a Bernoulli process. Each trial is called a ­Bernoulli trial.

3.2 Binomial (Bernoulli) Distribution

This process must possess the following ­properties:

1. The experiment consists of n repeated trials.
2. Each trial results in an outcome that may be classified as a success or a failure which are mutually exclusive.
3. The probability of success, denoted by p, ­remains constant from trial to trial.
4. The repeated trials are independent. ...