Paper 4: Fundamentals of Business Mathematics & Statistic

FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS I 10.13

5 8 5

256 1

256 C

⎛⎞⎜ × ⎟⎟

⎜⎜⎝⎠⎟⎟ 56

6 8 6

256 1

256 C

⎛⎞⎜ × ⎟⎟

⎜⎜⎝⎠⎟⎟ 28

7 8 7

256 1

256 C

⎛⎞⎜ × ⎟⎟

⎜⎜⎝⎠⎟⎟ 8

8 8 8

256 1

256 C

⎛⎞⎜ × ⎟⎟

⎜⎜⎝⎠⎟⎟ 1

10.3 POISSON DISTRIBUTION

Poisson distribution was derived in 1837 by a French mathematician Simeon D Poisson (1731-1840). In binomial
distribution, the values of p and q and n are given. There is a certainty of the total number of events; in
other words, we know the number of times an event does occur and also the times an event does not
occur, in binomial distribution. But there are cases where p is very small and n is very large, then calculation
involved will be long. Such cases will arise in connection with rare events, for example.

1. Persons killed in road accidents.


2. The number of defective articles produced by a quality machine,


3. The number of mistakes committed by a good typist, per page.


4. The number of persons dying due to rare disease or snake bite etc.


5. The number of accidental deaths by falling from trees or roofs etc.
   In all these cases we know the number of times an event happened but not how many times it does not
   occur. Events of these types are further illustrated below :


6. It is possible to count the number of people who died accidently by falling from trees or roofs, but we
   do not know how many people did not die by these accidents.


7. It is possible to know or to count the number of earth quakes that occurred in an area during a
   particular period of time, but it is, more or less, impossible to tell as to how many times the earth
   quakes did not occur.


8. It is possible to count the number of goals scored in a foot-ball match but cannot know the number
   of goals that could have been but not scored.


9. It is possible to count the lightning flash by a thunderstorm but it is impossible to count as to how many
   times, the lightning did not flash etc.
   Thus n, the total of trials in regard to a given event is not known, the binomial distribution is inapplicable,
   Poisson distribution is made use of in such cases where p is very Small. We mean that the chance of
   occurrence of that event is very small. The occurrence of such events is not haphazard. Their behaviour can
   also be explained by mathematical law. Poisson distribution may be obtained as a limiting case of binomial
   distribution. When p becomes very small and n is large, Poisson distribution may be obtained as a limiting
   case of binomial probability distribution, under the following conditions :


10. p, successes, approaches zero (p → 0)


11. np = m is finite.
    The poisson distribution is a discrete probability distribution. This distribution is useful in such cases where the
    value of p is very small and the value of n is very large. Poisson distribution is a limited form of binomial