BINOMIAL DISTRIBUTION IN STATISTICS......

BINOMIAL DISTRIBUTION IN STATISTICS......

1. BINOMIAL DISTRIBUTION

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 2 3. If we want to toss a coin ten times then the sample space will be 1024 i.e 2 10 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  n C x  = n!/x!(n-x)!. 

7. FOR BINOMIAL DISTRIBUTION Mean , μ = np Variance, σ 2  = 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 )