Binomial distribution :Here we are going to give you all the content related to binomial distribution ,probability mass function(pdf) of binomial distribution, its mean ,variance and also cumulative distribution function (cdf) of binomial distribution.

What is Binomial distribution??

It is a discrete probability distribution (such a distribution represent data that has a finite countable number of outcomes)that gives only two possible outcomes  in an experiment. For example, tossing of a coin gives two outcomes :head or tail

In binomial distribution there are two parameters n and p where n stands for number of times experiment runs and p stands for probability of any one outcome.

Suppose a coin is thrown randomly 7 times , then the probability of head for anyone throw is ½ . so, you have a binomial distribution of n=7 and p=1/2

When n=1 then binomial distribution is Bernoulli distribution.

Assumptions of binomial distribution

In binomial distribution,

1. Experiment consists of n identical and independent trials.
2. Each trail results one of two outcome- success or failure.
3. Probability of all trials i.e P(Success)=p ,P(Failure)=1-p=q

Example when assumption do not hold:

Here are some examples of binomial distribution when assumptions do not hold.

1. Bags contains 3 red balls and 4 green balls . Select 4 balls with replacement ,x is number of red balls.
2. Basketball player shoots 10 free throws.

The binomial distribution can be approximated by the normal distribution when n is large and p is not too close to 0 or 1.

some possible frequently asked questions based on binomial distribution are:

What is the name of the distribution that is a special case of the binomial distribution when the number of trials is one?

Bernoulli

What is the name of the parameter that represents the probability of success in each trial of a binomial experiment?

p

What is the name of the graph that shows the probabilities of different values of a binomial random variable?

Histogram