BINOMIAL DISTRIBUTION IN STATISTICS......
- 2. • In probability theory the binomial distribution is the discrete probability distribution that gives only two possible results in an experiment, either Success or Failure. • For example, if we toss a coin, there could be only two possible outcomes: heads or tails, and if any test is taken, then there could be only two results: pass or fail. This distribution is also called a binomial probability distribution. • There are two parameters n and p used here in a binomial distribution. The variable ‘n’ states the number of times the experiment runs and the variable ‘p’ tells the probability of any one outcome..
- 3. • Suppose you are tossing a coin 3 times • We can easily find the probability for getting 2 heads i.e 3/8. and the sample space will be 8 i.e 23.If we want to toss a coin ten times then the sample space will be 1024 i.e 210 • So in that case we use Binomial distribution. • A single success/failure test is also called a Bernoulli trial or Bernoulli experiment, and a series of outcomes is called a Bernoulli process.
- 4. EXAMPLES • Taking a survey of positive and negative reviews from the public for any specific product or place. • By using the YES/ NO survey, we can check whether the number of persons views the particular channel. • To find the number of male and female employees in an organisation.
- 5. • The binomial distribution formula is for any random variable X, given by;
- 6. • n = the number of experiments • x = 0, 1, 2, 3, 4, … • p = Probability of Success in a single experiment • q = Probability of Failure in a single experiment = 1 – p • The binomial distribution formula can also be written in the form of n-Bernoulli trials, where nCx = n!/x!(n-x)!.
- 7. FOR BINOMIAL DISTRIBUTION • Mean, μ = np • Variance, σ2 = npq • Standard Deviation σ= √(npq) • Where p is the probability of success • q is the probability of failure, where q = 1-p
- 8. Properties of Binomial Distribution The properties of the binomial distribution are: • There are two possible outcomes: true or false, success or failure, yes or no. • There is ‘n’ number of independent trials or a fixed number of n times repeated trials. • The probability of success or failure remains the same for each trial. • Only the number of success is calculated out of n independent trials. • Every trial is an independent trial, which means the outcome of one trial does not affect the outcome of another trial.
- 9. Q1.If a coin is tossed 5 times, find the probability of: • (a) Exactly 2 heads • (b) At least 4 heads.
- 10. SOLUTION:a)