Department of Mathematicscoretheory
PROBABILITY AND STOCHASTIC PROCESS
MAT 2136
Syllabus
- 01Probability: Basic concepts -Random Experiments, Sample space, Elementary and compound events, Algebra of events, Classical definition of probability and its limitations, relative frequency approach, Conditional Probability and Independence, Multiplication theorem, Bayes' Theorem (with proof) and its applications
- 02Random Variables, one and two dimensional, with marginal and conditional probability distributions. Expectation of r.v. s, functions of random variables, M.G.F.
- 03Discrete distributions, Limiting Distributions
- 04Continuous univariate distributions
- 05Sampling: Population and Sample, Complete enumeration v/s sample surveys - merits and demerits. Need for sampling, random and non-random sampling, limitations of non-random sampling and judgment sampling, Errors in sampling. Parameter and statistic, Unbiasedness, variance and precision of estimators, pilot survey, determination of sample size, Sampling variances, standard errors, Sampling Distributions-Definition and derivation of students' t, Chi-squared and F- distributions using transformation of random variables – their properties
- 06Estimation & Inference: Limit theorems - Markov's inequality, statement and proof of Chebychev's inequality, sequence of random variables, convergence in probability: basic results (without proof), Weak law of large numbers, central limit theorem for i. i. d. random variables and its application. Methods of estimations and characteristics of an ideal estimator, testing of hypothesis – basic concepts-type I & II errors, size & power of the test, testing for equality of mean/ two means, independence of attributes, proportions, testing for goodness of fit. Confidence intervals also to be covered
References
- Gupta, S. C., & Kapoor, V. K. (2002). Fundamental of Mathematical Statistics. Sultan Chand & sons.
- Rohatgi, V. K. (2002). An Introduction to Probability theory and Mathematical Statistics. Wiley Eastern Limited.
- Ross, S. M. (2003). Introduction to Probability Models. 10e, Academic Press, UK.
- Mukhopadhyay P. (1998): Theory and Methods of Survey Sampling, Prentice-Hall of India
- Medhi, J. (2006). Statistical Methods: An Introductory Text. New Age International(P) Limited, New Delhi.
- P L Meyer: Introductory Probability and Statistical Applications 2Ed (2017), Wiley.
Credits Structure
3Lecture
1Tutorial
0Practical
4Total