Welcome to the course page for Probability and Statistics. Here, I will compile everything related to this course that my students will require.
Course name : Probability and Statistics(MAT-2020/CS-1209/PHY-1208-2)
Timings : Monday and Wednesday, 8:30 AM - 10:00 AM.
Classroom Number : AC-04-LR-302.
Syllabus (as per Mathematics Handbook): Frequency and axiomatic definition of probability, random experiments with equally likely finite outcomes, Inclusion exclusion principle. General finite sample spaces, infinite sample spaces. Concept of probability spaces and construction of probability measures. Conditional probability, Bayes theorem, Independence of events. Random variable (discrete), probability mass function and distribution function. Examples: Bernoulli, Binomial, Poisson, Geometric distributions. Expectation and variance of a random variable, sum law and product law of expectation, moment generating functions. Random vector (discrete), joint distribution, Marginal distributions, joint moment generating functions, covariance, Multinomial distributions. Continuous random variables, density functions, distribution functions, expectation, variance, moment generating function, example: uniform, normal, and exponential. Continuous random vector, joint density function, joint distribution function, conditional density, example: multivariate normal. Markov’s and Chebyshev’s inequalities. The law of large numbers and Central Limit theorem (without proof). Descriptive statistics, Distribution of sampling statistics, Parameter Estimation and basics of hypothesis testing. Simple linear regression with one regressor (only if time permits).
Recommended Books (as per Mathematical Handbook) :
S. M. Ross: First Course in Probability, Pearson.
S. M. Ross: Introduction to Probability and Statistics for Engineers and Scientists.
J. L. Devore: Probability and Statistics for Engineering, Cengage, 2012.
V. K. Rohatgi, E. S. Saleh: An Introduction to Probability and Statistics, Wiley-Blackwell, 3rd edition, 2015.
Useful Links for Students of this Course
Notes on Probability and Statistics by Prof. Manjunath Krishnapur, Mathematics Department, IISc.
Interactive Version of the above lecture notes by Prof. Siddhartha Gadgil, Mathematics Department, IISc.
The assignments for this course can be found in this folder.
The lecture notes for this course can be found in this folder.
The final exams, their solutions and a hard problem sheet can be found in this folder.