Page 284 - DCOM203_DMGT204_QUANTITATIVE_TECHNIQUES_I

Unit 13: Binomial Probability Distribution

3. The total number of possible values of the random variable are n + 1. The successive Notes
n
n
n
n
n
n
binomial coefficients are C , C , C , .... C Further, since C = C , these
0 1 2 n r n- r
coefficients are symmetric.
The values of these coefficients, for various values of n, can be obtained directly by using
Pascal’s triangle.
Pascal’s Triangle

We can note that it is very easy to write this triangle. In the first row, both the coefficients
1
1
will be unity because C = C . To write the second row, we write 1 in the beginning
0 1
and the end and the value of the middle coefficients is obtained by adding the coefficients
of the first row. Other rows of the Pascal’s triangle can be written in a similar way.
4. (a) The shape and location of binomial distribution changes as the value of p changes
for a given value of n. It can be shown that for a given value of n, if p is increased
gradually in the interval (0, 0.5), the distribution changes from a positively skewed
to a symmetrical shape. When p = 0.5, the distribution is perfectly symmetrical.
Further, for larger values of p the distribution tends to become more and more
negatively skewed.
(b) For a given value of p, which is neither too small nor too large, the distribution
becomes more and more symmetrical as n becomes larger and larger.

13.3.2 Uses of Binomial Distribution

Binomial distribution is often used in various decision making situations in business. Acceptance
sampling plan, a technique of quality control, is based on this distribution. With the use of
sampling plan, it is possible to accept or reject a lot of items either at the stage of its manufacture
or at the stage of its purchase.

Decision Analysis
Notes

Decision making is needed whenever an individual or an organization (private or public)
is faced with a situation of selecting an optimal (or best in view of certain objectives)
course of action from among several available alternatives. For example, an individual
may have to decide whether to build a house or to purchase a flat or live in a rented
accommodation; whether to join a service or to start own business; which company’s car
should be purchased, etc. Similarly, a business firm may have to decide the type of technique
to be used in production, what is the most appropriate method of advertising its product,
etc.
The decision analysis provides certain criteria for the selection of a course of action such
that the objective of the decision maker is satisfied. The course of action selected on the
basis of such criteria is termed as the optimal course of action.

LOVELY PROFESSIONAL UNIVERSITY 279