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THEORY (30 Hours)

UNIT-I (7 Hours)
Probability: Introduction, random experiments, sample space, events and algebra of events.
Definitions of Probability – classical, statistical, and axiomatic. Conditional Probability, laws of
addition and multiplication, independent events, theorem of total probability, Bayes‘ theorem and
its applications.

UNIT-II (8 Hours)
Random variables: discrete and continuous random variables, p.m.f., p.d.f. and c.d.f., illustrations
and properties of random variables, univariate transformations with illustrations. Two dimensional
random variables: discrete and continuous type, joint, marginal and conditional p.m.f, p.d.f., and
c.d.f., independence of variables.

UNIT-III (7 Hours)
Mathematical Expectation and Generating Functions: Expectation of single and bivariate random
variables and its properties. Moments and Cumulants, moment generating function, cumulant
generating function and characteristic function. Uniqueness and inversion theorems (without
proof) along with applications. Conditional expectations.

UNIT-IV (8 Hours)
Standard discrete probability distributions: Uniform, Binomial, Poisson, geometric, along with
their properties and limiting/approximation cases. Standard continuous probability distributions:
uniform, normal, exponential, beta and gamma along with their properties and
limiting/approximation cases.

PRACTICAL (30 Hours)

1. Fitting of binomial distributions
2. Fitting of Poisson distributions
3. Fitting of Normal distributions
4. Application problems based on binomial, Poisson, and Normal distribution

SUGGUESTED READINGS:

1. Goon A.M., Gupta M.K. and Dasgupta B. (2002): Fundamentals of Statistics, Vol. I, 8th
Edn. The World Press, Kolkata.
2. Gupta, S. C. and Kapoor, V.K. (2008): Fundamentals of Mathematical Statistics,
th
4 Edition (Reprint), Sultan Chand &Sons
3. Hogg, R. V.,Tanis,E.A.andRaoJ.M.(2009):ProbabilityandStatisticalInference, Seventh Ed,
Pearson Education, New Delhi.
4. Miller, Irwinand Miller, Marylees (2006): JohnE. Freund‘s Mathematical Statistics with
th
Applications, (7 Edn.), Pearson Education, Asia.
5. Mood, A.M. Graybill, F.A. and Boes, D.C. (2007): Introduction to the Theory of Statistics,
3rd Edn., (Reprint), Tata McGraw-Hill Pub. Co. Ltd.
6. Myer, P.L. (1970): Introductory Probability and Statistical Applications, Oxford & IBH
Publishing, New Delhi

Env.321 Environmental Science and Impact Assessment 2+1

LEARNING OBJECTIVES:

The primary objective of this course is to introduce:

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