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.