Paper 4: Fundamentals of Business Mathematics & Statistic

FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS I 10.17

=

4 4423

e− (^14) 2! 3!

⎛⎞⎜ ⎟⎟

⎜⎜⎜⎝⎠++ +⎟⎟

= e–4 (1+4+8+10.67)

= e–4×23.67

= 0.01832 × 23.67

= 0.4336

Example 18 :
Comment on the following :
For a Poisson Distribution, Mean = 8 and variance = 7

Solution :
The given statement is wrong, because for a. Poisson Distribution
mean and variance are equal.

10.3.1. Fitting a Poisson Distribution
When we want to fit a Poisson Distribution to a given frequency distribution, first we have to find out the
arithmetic mean of the given data i.e., X=m When m is known the other values can be found out easily. This
is clear from the following illustration :
N(P 0 ) = Ne–m

N(P 1 ) = N(Po)×m 1

N(P 2 ) = N(P 1 )×m 2

N(P 3 ) = N(P 2 )×m 3

N(P 4 ) = N(P 3 )×m 4 and so on

Example 19 :

100 Car Radios are inspected as they come off the production line and number of defects per set is recorded
below :

No. of Defects 0 1 2 3 4

No. of sets 79 18 2 1 0

Fit a Poisson Distribution to the above data and calculate the frequencies of 0, 1, 2, 3, .and 4 defects.
(e–0.25=0.779)