3. A discrete Probability Distribution
Derived by French mathematician Simeon Denis
Poisson in 1837
Defined by the mean number of occurrences in a
time interval and denoted by λ
Also known as the Distribution of Rare Events
Poisson Distribution
Simeon D. Poisson (1781-
1840)
4. Works when binomial calculation becomes impractical (No. of
trials>probability of success),
Applied where random events in space or time are expected to occur.
Deviation indicates some degree of non-randomness in the events
Example: Number of earthquakes per year.
Cont’d…
5. Requirements for a Poisson Distribution
RIPS
Random
Proportional
Simultaneous
Independent
6. Assumptions
The probability of occurrence of an event is constant for
all subintervals:
There can be no more than one occurrence in each
interval
Occurrence are independent .
8. Mathematical Calculations
#If the average number of accidents at a particular intersection in
every year is 18. Then-
(a) Calculate the probability that there are exactly 2 accidents
occurred in this month.
(b) Calculate the probability that there is at least one accident
occurred in this month.
9. There are 12 months in a year, so = 12
18
= 1.5 accidents per month
P(X = 3) =
!x
e x
!2
5.1 25.1
e
= 0.2510
(a) Calculate the probability that there are exactly 2
accidents occurred in this month.
10. (b) Calculate the probability that there is at least one
accident occurred in this month.
P(X ≥ 1 ) = P(X=1) + P(X=2) + P(X=3) + …. Infinite.
So… Take the complement: P(X=0)
!x
e x
!0
5.1 05.1
e
5.1
e
= 0.223130…