Page 343 - DECO504_STATISTICAL_METHODS_IN_ECONOMICS_ENGLISH

Statistical Methods in Economics

Notes Example 23: A survey conducted over the last 25 years indicated that in 10 years, the winter was
mild, in 8 years it was cold and in the remaining 7 it was very cold. A company sells
1000 woolen coats in a mild year, 1300 in a cold year and 2000 in a very cold year. If a
woolen coat costs Rs. 173 and is sold for Rs. 248, find the yearly expected profit of the
company.
Solution:
State of Nature Prob. P (X) Sale of woollen coat Profit (X)

10
Mild winter = 0.4 1000 1000 × (248 – 173)
25

8
Cold winter = 0.32 1300 1300 × (248 – 173)
25

7
Very cold winter = 0.28 2000 2000 × (248 – 173)
25
∴ Expected profit is given by
E (X) = 1000 × 75 × 0.4 + 1300 × 75 × 0.32 + 2000 × 75 × 0.28
= 30,000 + 31,200 + 42,000 = Rs. 1,03,200
Self-Assessment

1. Which of the following statements are true or false:
(i) The classical approach to probability is the oldest and simplest.
(ii) The probability of throwing eight with a single dice is 1/6.
(iii) The modern probability theory has been developed automatically in which probability is an
undefined concept.
(iv) In most field of research, a priori probability is employed.
(v) Dependent events are those in which the outcome of one does not affect and is not affected
by the other.
26.3 Summary

• “It is likely that the particular teacher may not come for taking his class today”; “there is a
chance that the particular student may stand first in the university examination”; “it is possible
that the particular company may get the contract which it bid last week”; “most probably I
shall be returning within a week”; “it is possible that he may not be able to join his duty”. In all
the above statements, the terms—possible, probably, likely, chance, etc., convey the same
meaning, i.e., the events are not certain to take place. In other words, there is involved an
element of uncertainty or chance in all these cases. A numerical measure of uncertainty is
provided by the theory of probability. The aim of the probability theory is to provide a measure
of uncertainty. The theory of probability owes its origin to the study of games of chance like
games of cards, tossing coins, dice, etc. But in modern times, it has great importance is decision
making problems.
• In simple words, probability is the likelihood or chance that a particular event will or will not
occur. The theory of probability provides a quantitative measure of uncertainty or likelihood of
occurrence of different events resulting from a random experiment, in terms of quantitative
measures ranging from 0 to 1. This means that the probability of a certain event is 1 and the
probability of an impossible event is 0. In other words, a probability near 0 indicates that an
event is unlikely to occur whereas a probability near 1 indicates that an event is almost certain

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