Binomial Distribution is used when there are exactly two mutually exclusive outcome of trial, These outcomes are appropriate labeled success and failure.
Characteristics
1. It is a discrete distribution.
2. Trials are finite (and not very large), performed repeatedly for ‘n’ times.
3. Each trial (random experiment) should be a Bernoulli trial, the one that results in either success or failure.
4. Probability of success in any trial is ‘p’ and is constant for each trial.
5. Sampling is done with replacement.
6. All trials are independent.
Assumption
Binomial distribution deals with only two events Probability of success P and Probability of failure Q = 1- P So here we assume that P (Probability of success will never change as different trails take place. So sampling is always done with replacement in binomial distribution.
Application of Bernoulli distribution
Situations where Bernoulli distribution is commonly used are
1. Sex of newborn child; Male = 0, Female = 1 say.
2. Items produced by a machine are Defective or Non-defective.
3. During next flight an engine will fail or remain serviceable.
4 Student appearing for examination will pass or fail.
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