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) = nCx px (1-p)n-x Or P(X=x) = nCx px (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 = (Mx(t)) = (pet + 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.

9. Quality Control

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11. Quality Control

12. THANK - YOU