Binomial Distribution in Probability and Statistics

Bernoulli Trials

Many experiments have only two outcomes, for example if you are tossing a coin you will get head or tail. If you rolling a dice you will have number on the face which may be an even or an odd number.

When a company manufactures items, so item may be defective or it may be non-defective.

It is important to understand that you have to name one outcome as success and other one as failure.

When experiment you perform like tossing a coin, it is called a trial.

1- Bernoulli trials are finite

2- Each trial is independent

3-Every trial has only two outcomes success and failure

4-Probability of the success and failure in each trial is the same

Binomial Distribution-

If there are x successes in n trials, then the probability of each n-tuple with x success and n-x failures will be

px (1-p)n-x

On the other hand, there are Cnx tuples with x successes and n-x failures in n trials.

Cnx    px (1-p)n-x

Where x= 0, 1, 2, 3 ….n

A random variable X is said to follow Binomial Distribution if it follows the probability mass function

f(x)= Cnx    px (1-p)n-x

And it would be written as

f(x)= P(X=x)= Cnx    px (1-p)n-x

Binomial random variable has two parameters p and n and usually written as X~Bin(n,p).

See video to understand clearly.

 

 

 

 

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