Binomial Distribution
Binomial distribution was discovered by swiss mathematician James Bernonulli, so this distribution is called as Bernoulli distribution also, this is a discrete frequency distribution.
Assumptions of a binomial Distribution
1. The random experiment is performed repeatedly with a fixed and finite number of trials. N is denoted by number of trials.
2. There are two mutually exclusive possible outcomes on each trial which are known as success and failure success is denoted by whereas failure is denoted by q, and p+q = 1 or q=1-p1.
3. The outcomes of any given trial does not affect the outcomes on subsequent trials means the trials are independent.
4. The probability of success and failure (p&q) remains constant from trial to trial. If in any distribution the p& q does not remain constant that distribution cannot be a binomial distribution, For example the probability of getting head must remain the same in each toss i.e. ½ similarly the probability of drawing 4 balls from a bag containing 6 red and 10 white balls does not change in successive draws with replacement, hence it will be called as binomial distribution .But in contrary to this, if balls are not replaced after each trail then it will not be a binomial distribution.
5. If all above assumptions are satisfied , the probability of exactly r successes in n trials is given by
6. P(n=r)=^{n}_{ }c_{r}p^{r}q^{n-r}