The document discusses the binomial and Poisson distributions. The binomial distribution describes the probability of success in a fixed number of yes/no trials, while the Poisson distribution models the occurrence of rare events. Examples of applications include defective items in manufacturing and accidents. Key characteristics of both distributions including their formulas are provided. The document concludes by noting the Poisson distribution is useful for modeling rare events with small probabilities of success.

1. Binomial and Poisson
Distribution
Under the guidance of
Sundar B. N.
Asst. Prof. & Course Co-ordinator
GFGCW, PG Studies in Commerce
Holenarasipura
Harshitha R J
2nd M.COM

2. INTRODUCTION
CONTENT OF THE BODY
CONCIUSION
REFERENCE

3. 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,.
Poisson distributionis a discrete probability distribution amd it is widely used
in stastistical work this distribution was developed by French mathematician
dr .simon denis poisson in 1837 amd the distribution is named after HIM
.THE POISSON DISTRIBUTION IS USED IN THOSE SITUATION WHERE
THE PROBABILITY OF THE HAPPENING OF AN EVEMT IS VERY SMALL
THE EVENT RARELY OCCURS.
EXAMPLE,THE PROBABILITY 0F DEFECTIVE ITEMS IN A
MANUFACTURING CAMPANY IS VERY SMALL ,THE PROBABILITY OF
THE ACCIDENTS ON ROAD IS VERY SMALL ,ETC.ALL THESE ARE
EXAMPLES OF SUCH EVENTS WHERE THE PROBABILITY OF
OCCURREMCE IS VERY SMALL
THE

4. The Binomial Distribution
Probability
Distributions
Discrete
Probability
Distributions
Binomial
Poisson
Hypergeometric

5. Binomial distribution
What is binomial distribution
The bionomial disrtbution is a probability.distribution that
summarizes the likelihood that summarizes the likelihood that a
value will take one of two indepemdent value under a given set of
parameters or assumption .the underlying assumptions of the
binomial distribution are that there is only one outcome for each
trail ,that each traial has the same probability of success, and that
each trial is mutually exclusive ,or independent of each other.

6. Example of bionomial distribution
The binomial distribution is calculated by
multiplying the probability of success raised to the
power of the number of success and the probability
of failure raised to the power of the different
between the number of success and the number of
trails . Then, multiply the product by the
combination between the number of trails and the
number of success

7. Binomial distubition formula
The binomial distribution formula in probability
binomial distribution
formula P2(x)=nCr.𝑝𝑟 1 − 𝑝 𝑛−𝑟
Or P(x)=[n!/r!(n-r)!].𝑝𝑟
(1 − 𝑝)𝑛−𝑟

8. WHERE
 n =Total number of events.
r = Total number of successful events.
P =probability of success on a single trial.
nCr =[n!/r!(n-r)]!
1-p = probability of failure.

9. Binomial Distribution Characteristics
 Mean
µ=E(x)=np
Variance and Standard Deviation
σ2
= 𝑛𝑝𝑞
σ=√npq
Where n= sample size
p= probability of success
q= (1-p)=probability of failure

10. POISSON distribution
 What is the poisson distribution ?
The poisson distribution is a tool used in probability theory statistics to
predict the amount of variation from a know average rate of occurrence
,within a given time frame
In other words, if the average rate at which a specific event happens within a
specified time frame is known or can be determined, then the Poisson
Distribution

11. The history of the poisson
distribution
Like many statistical tools and probability metrics,the
poisson distribution was originally applied to the world of
gambling.in 1830,French mathematician simeon denis
poisson developed the distribution to indicate the low to
high spread of the probable number of times that a gambler
would win at a gambling game –such as baccarat-within a
large number of times that the game was played .
(unfortunately,thegambler paid no heed to poisson,s
prediction of the probabilities of obtaining only a
certain number of wins,and lost heavily.)

12. THE DISTRIBUTION FORMULA
Below is the poisson distribution formula,where the mean (
average)number of events within a specified time frame is
designated by µ.the probability formula is

13.  Formula
where;
x= number of times and event occurs during the time
period
e(Euler’s number=the base of natural logarithms) is
approx. 2.72
x!= the factorial of x(for example, if x is 3 then
x!=3*2*1=6)
P(x;µ)=(𝑒−µ)(µ𝑥)/x!

14. Examples: Business Uses of the Poisson
Distribution
 The Poisson Distribution can be practically applied to several
business operations that are common for companies to engage
in. As noted above, analyzing operations with the Poisson
Distribution can provide company management with insights
into levels of operational efficiency and suggest ways to
increase efficiency and improve operations.
 Here are some of the ways that a company might utilize
analysis with the Poisson Distribution.

15. Characteristics of the Poisson
Distribution:
 The outcomes of interest are rare relatives to the possible
outcomes
 The average number of outcomes of interest per time or
space interval is λ.
 The number of outcomes of interest are random, and the
occurrence of one outcome does not influence the
chances of another outcome of interest.
 The probability of that an outcome of interest occurs in a
given segment is the same for all segments.

16. Poisson Distribution Characteristics
 Mean
µ=λt
Variance and Standard Deviation
σ2
=λt
σ=√λt
Where λ= number of successes in a segment of unit size
t= the number of the segment of inter̥est

17. conclusion
IF STUDENTS DID JUST RANDOMLY GUESS WHICH STATEMENT WAS
FALSE ,WE’D EXPECT THE RANDOM VARIABLE X TO FOLLOW A
BINOMIAL DISTRIBUTION ?
CAN BE CONCLUDE THAT STUDENTS DID NOT GUESS THE FALSE
STATEMENTS RANDOM
In conclusion ,
we can say that, the poisson
distribution is useful in rare events where the
probability of success (p)is very small and
probability of failure (q) is very large and value of n
is very large.

18. BIBLIOGRAPHY
Binomial distribution definition formula in probability topic related to
binomial probability distribution http://www.Investopedia.com/terms
/b/binomialdistribution.asp
Poisson distribution business uses of poisson definition characters
https://corporatefinanceinstitute.com/resources/knowledge/other/p
oisson-distribution/
https://www.google.com/imgres