Binomial-Distribution & It’s Application.pptx

Binomial distribution applications

1. Binomial-Distribution & It’s Application Group – 6 NAME Roll No. Mayur Kasat MBA202224-090 Neelmani Singh MBA202224-098 Nishant Jha MBA202224-100 Palak Jain MBA202224-101 Rounak Rathi MBA202224-132

2. Origin Binomial Distribution was discovered by the Swiss mathematician Jacob Bernoulli (1654-1705) in a proof, published posthumously in 1713

3. What? The binomial distribution is the discrete probability distribution that gives only two possible results in an experiment, either Success or Failure. Consider a fixed number of mutually independent Bernoulli trials where ‘p’ denotes the probability of success. So a random variable called Bernoulli random variable represents the total no. of success in the ‘n’ independent Bernoulli trial. f(X) = P(X=x) P(X=x) =  n C x  p x  (1-p) n-x Or P(X=x) =  n C x  p x  (q) n-x X ~ Binomial(n,p) where; 0<p<1

4. Properties Of Binomial Distribution 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 successes is calculated out of n independent trials. Every trial is an independent trial, meaning the outcome of one trial does not affect the outcome of another.

5. Characteristic Mean (µ) = np Variance ( σ² ) = np*(1-p) = npq MGF = (M x (t)) = (pe t + 1 – p) x

6. Applications Of Binomial Distribution

7. Market Research Businesses often conduct surveys to gather data on consumer behavior or preference. To estimate the proportion of consumers who prefers certain products or services. To model the probability of a consumer responding to a campaign, given the target audience size and success rate of the movement. Probability of a certain no. of sales in a fixed period based on historical data and market trends

8. Medical Field Medical trials to determine the probability of successes or failures in a given no. of patients. For example, a drug company may test a new drug on a group of 100 patients to calculate a certain number of patients responding to a drug. In Genetics, the distribution can be used to model the distribution of genotypes in a population. The probability of a particular genotype is the probability of success.

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