Probability and Statistics | Department of Mathematics

Probability and Statistics

Core course for BSc (Research) Economics. Students of BSc (Research) Mathematics or any B.Tech. program are not allowed to credit this course.

Prerequisites: Calculus I (MAT 101)

Overview: Probability is the means by which we model the inherent randomness of natural phenomena. This course introduces you to a range of techniques for understanding randomness and variability, and for understanding relationships between quantities. The concluding portions on Statistics take up the problem of testing our theoretical models against actual data, as well as applying the models to data in order to make decisions. This course is a prerequisite for later courses in Advanced Statistics, Stochastic Processes and Mathematical Finance.

Detailed Syllabus:

1.    Probability: Classical probability, axiomatic approach, conditional probability, independent events, addition and multiplication theorems with applications, Bayes’ theorem.
2.    Random Variables: Probability mass function, probability density function, cumulative density function, expectation, variance, standard deviation, mode, median, moment generating function.
3.    Some Distributions and their Applications: Uniform (discrete and continuous), Bernoulli, Binomial, Poisson, Exponential, Normal.
4.    Sequences of Random Variables: Chebyshev’s Inequality, Law of Large Numbers, Central Limit Theorem, random walks.
5.    Joint Distributions: Joint and marginal distributions, covariance, correlation, independent random variables, least squares method, linear regression.
6.    Sampling: Sample mean and variance, standard error, sample correlation, chi square distribution, t distribution, F distribution, point estimation, confidence intervals.
7.    Hypothesis Testing: Null and alternate hypothesis, Type I and Type II errors, large sample tests, small sample tests, power of a test, goodness of fit, chi square test.

Main References:
•    A First Course in Probability by Sheldon Ross, 6th edition, Pearson.
•    John E. Freund’s Mathematical Statistics with Applications by I. Miller & M. Miller, 7th edition, Pearson, 2011.

Other References:
•    Elementary Probability Theory: With Stochastic Processes and an Introduction to Mathematical Finance by Kai Lai Chung and Farid Aitsahlia, 4th edition, Springer International Edition, 2004.
•    Introduction to the Theory of Statistics by Alexander M. Mood, Franklin A. Graybill and Duane C. Boes, 3rd edition, Tata McGraw-Hill, 2001.

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