10.14 I FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS

Theoretical Distribution

distribution as n moves towards infinity and p moves towards zero and np or mean remains constant. That

is, a poisson distribution may be expected in cases where the chance of any individual event being a

success is small.

The Poisson distribution of the probabilities of Occurrence of various rare events (successes) 0, 1, 2, .... given

below:

Number of success Probabilities p (X)

0e–m

1 me–m

2

2

2!

me−m

3

3

3!

me−m

r!

merm

r

−

n!

menm

n

−

e = 2.71828

m = average number of occerence of given distribution

The Poisson distribution is a discrete distribution with a parameter m. The various constants are :

1. Mean = m = p


2. Stanlald Deviation = m


3. Variance = m
   Example 13 :
   A book contains 100 misprints distributed randomly throughout its 100 pages. What is the probability that a
   page observed at random contains atleast two misprints. Assume Poisson Distribution.
   Solution:
   m= Total Number of misprints 100Total number of page 100==^1
   Probability that a page contain at least two misprints

Pr()≥ (^2) = 1 – [p (0) + p (1)]
p(r)=!
merm
r
−
p(0) =
(^111011)
0! 2.7183
e e
e
− −