Binomial distribution
Download as PPTX, PDF9 likes13,109 views
The document defines and explains the binomial distribution. It was developed by James Bernoulli in 1700 and describes the probability of success in a fixed number of binary trials where the probability of success is the same for each trial. The key points are: - It gives the probability of x successes in n trials where the probability of success p is constant for each trial. - The formula to calculate binomial probability is P(X) = nCx * px * q(n-x) where n is the number of trials, x is the number of successes, p is the probability of success, and q is the probability of failure (1 - p). - The mean is np, the variance is np
Binomial distribution
- 1. 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) = nCx Px 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. STATISTICS OF THE BINOMIAL DISTRIBUTION 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.
- 9. Thank You