Page 273 - DCOM203_DMGT204_QUANTITATIVE_TECHNIQUES_I

Quantitative Techniques – I

Notes The knowledge of the theoretical probability distribution is of great use in the understanding
and analysis of a large number of business and economic situations. For example, with the use
of probability distribution, it is possible to test a hypothesis about a population, to take decision
in the face of uncertainty, to make forecast, etc.
Theoretical probability distributions can be divided into two broad categories, viz. discrete and
continuous probability distributions, depending upon whether the random variable is discrete
or continuous. Although, there are a large number of distributions in each category, we shall
discuss only some of them having important business and economic applications.

Did u know? In order to discuss the applications of probability to practical situations, it is
necessary to associate some numerical characteristics with each possible outcome of the
random experiment. This numerical characteristic is termed as random variable.

13.1 Concept of Probablity Distribution

A probability distribution is a rule that assigns a probability to every possible outcome of an
experiment.
In order to discuss the applications of probability to practical situations, it is necessary to
associate some numerical characteristics with each possible outcome of the random experiment.
This numerical characteristic is termed as random variable. Or we can say, An event whose
numerical value is determined by the outcome of an experiment is called a variate or often a
random variable.

Example: Three coins are tossed simultaneously. Write down the sample space of the
random experiment. What are the possible values of the random variable X, if it denotes the
number of heads obtained?
Solution:
The sample space of the experiment can be written as:
S = {(H,H,H), (H,H,T), (H,T,H), (T,H,H), (H,T,T), (T,H,T), (T,T,H), (T,T,T)}

We note that the first element of the sample space denotes 3 heads, therefore, the corresponding
value of the random variable will be 3. Similarly, the value of the random variable corresponding
to each of the second, third and fourth element will be 2 and it will be 1 for each of the fifth, sixth
and seventh element and 0 for the last element. Thus, the random variable X, defined above can
take four possible values, i.e., 0, 1, 2 and 3.
It may be pointed out here that it is possible to define another random variable on the above
sample space.

13.1.1 Probability Distribution of a Random Variable

Given any random variable, corresponding to a sample space, it is possible to associate
probabilities to each of its possible values. For example, in the toss of 3 coins, assuming that they
are unbiased, the probabilities of various values of the random variable X, defined in example
above, can be written as:

1 3 3 1
P X 0 ,P X 1 ,P X 2 and P X 3 .
8 8 8 8

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