Binomial distribution

Binomial distribution

1. Binomial Distribution By Dr. Satyanarayan Pandey Department of Management Studies BBMKU, Dhanbad

2. Introduction Binomial distribution was given by Swiss mathematician James Bernouli ( 1654-1705) in 1700 and it was first published in 1713. It is also known as ‘ Bernouli Distribution’.

3. DEFINITION Binomial distribution is a discrete probability distribution which is obtained when the probability p of the happening of an event is same in all the trials, and there are only two events in each trial .  E.g... The probability of getting a head, when a coin is tossed a number of times, must remains same in each toss i.e. P= 1/2.

4. CALCULATION OF BINOMIAL DISTRIBUTION It is a discrete probability distribution. Binomial Probability is calculated by following general formula- P(X) = n C x P x q (n-x ) Where , n = number of trials x = number of success p = Probability of success q = Probability of failure = 1 – p

5. CHARACTERISTICS OF BINOMIAL DISTRIBUTION  It is a discrete distribution which gives the theoretical probabilities. It depends on the parameter p or q, the probability of success or failure and n(i.e. The number of trials). The parameter n is always a positive integer. The distribution will be symmetrical if p=q. It is skew symmetric or asymmetric if p is not equal to q.

6. S TATISTICS OF THE BINOMIAL D ISTRIBUTION The statistics of the binomial distribution are: Mean= np , Variance= npq , and Standard deviation = √ npq The mode of the binomial distribution is equal to that value of x which has longer frequency.

7. CONDITIONS FOR BINOMIAL DISTRIBUTION The random experiment is performed repeatedly a finite and fixed number of times. The outcome of the random experiment(trials) results in the dichotomous classification of events . All the trials are independent . The probability of success in any trial is p and is constant for each trial. q = 1-p is then termed as the probability of failure and is constant for each trial.

8. Example E.g... If we toss a fair coin n times ( which is fixed and finite), then the outcome of any trial is one of the mutually exclusive events, viz , head(success) and tail(failure). Further, all the trials are independent, since the result of any throw of coin does not affect and is not affected by the result of other throws.

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