Page 92 - DMTH404_STATISTICS

Statistics

Notes 6.10 Review Questions

1. Define the term 'probability' by (a) The Classical Approach, (b) The Statistical Approach.
What are the main limitations of these approaches?

2. Discuss the axiomatic approach to probability. In what way it is an improvement over
classical and statistical approaches?
3. Distinguish between objective probability and subjective probability. Give one example
of each concept.
4. State and prove theorem of addition of probabilities for two events when (a) they are not
independent, (b) they are independent.
5. Explain the meaning of conditional probability. State and prove the multiplication rule of
probability of two events when (a) they are not independent, (b) they are independent.

6. Explain the concept of independence and mutually exclusiveness of two events A and B. If
A and B are independent events, then prove that A and B are also independent.
(b) For two events A and B it is given that
p b 
P A b g = 04, P B b g = , P A Bg = 06
.
.
(i) Find the value of p so that A and B are independent.
(ii) Find the value of p so that A and B are mutually exclusive.
7. Explain the meaning of a statistical experiment and corresponding sample space. Write
down the sample space of an experiment of simultaneous toss of two coins and a die.

Answers: Self Assessment

1. (a) 2. (c) 3. (d) 4. (b) 5. (b) 6. (c)

6.11 Further Readings

Books Introductory Probability and Statistical Applications by P.L. Meyer
Introduction to Mathematical Statistics by Hogg and Craig
Fundamentals of Mathematical Statistics by S.C. Gupta and V.K. Kapoor

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