Statistics-Poisson Distribution

1. Poisson Distribution
Presented By-
Gobinda Acharya (15)
Under the guidance of-
Mr. Sakti Ranjan Dash
Assistant Professor
Berhampur University
DEPARTMENT OF COMMERCE
BERHAMPUR UNIVERSITY, BHANJA BIHAR
September 1, 2021

2. Probability Distribution
• A probability distribution is a statistical function that describes all the possible values and
likelihoods that a random variable can take within a given range.
• A probability distribution is the statistical function that gives the probabilities of
occurrence of different possible outcomes for an experiment.
Poisson Distribution
• A poisson distribution is a probability distribution that is used to show how many times
an event is likely to occur over a specified period.
• This distribution was published in derivation by Simeon Denis Poisson in the year of 1837.
• The poisson distribution is a discrete function , meaningly that variable can take specific
value like 0,1,2 and 3 etc. with no fraction or decimal.
• It is a limiting form of the binomial distribution in which n (number of trials) becomes very
large and P (probability of success) is very very small.

3. Characterstics of Poisson Distribution
• The occurrence of the events is Independent.
• The number of occurrence is Infinite in a specified interval.
• It is a discrete function , meaningly that variable can take specific value like 0,1,2 and 3
with no fraction or decimal.
• Two event cannot occur at exactly same instant, instead each very small subinterval
one event either occurs or does not occur.( In any extremely small portion of interval ,
probability of two or more occurrences of the event is negligible.
Two important aspect why it differs from binomial distribution
• It operates continuously over some given amount of time , distance, area.
• It produces success which occur at random points in the specified time, distance, area.
These success are commonly referred to as occurrences.

4. Some of experiment was already done
• The number of soldier killed by horse kick each year 14 calvary corps over a 20 year
in 1898.
• The numbers of phone calls arriving at call centre within a minute was described by A.K.
Erlang.
• The number of road accident in a particular area over a specific period of time.
WHY we need Poisson distribution
• When chance of individual event success is very small .
• It is used to describe the behaviour of rare event.

5. Function of Poisson Distribution
P ( X = x)=
Where,
x = Number of occurrences
𝜆 = 𝑙𝑎𝑚𝑏𝑑𝑎 =Expected value = mean
e = Euler`s number ( the base of natural logarithm)
x! = factorial of x
𝜆𝑥. ⅇ−𝜆
𝑋!

6. Q.1) The average number of accidents in every year is 18.
calculate the probability that there are exactly 2 accidents in a month ?
Solution
Average accidents in a month = λ = 18/12 = 1.5 accidents per month
P ( X = x)=
P ( X = 2)=
=
=
= 0.2509
𝜆𝑥
. ⅇ−𝜆
𝑋!
1.52. 2.7183−1.5
2!
2.25 ∗ 0.2231
2
0.501975
2

7. THANK
YOU