Syllabus:
Random experiments, outcomes, sample space, events. Discrete sample spaces and probability models . Equally likely setup and combinatorial probability, examples. Combination of events: inclusion/exclusion, Boole's inequality.
Conditional probability: independence, law of total probability and Bayes theorem. Composite experiments: Polyas urn scheme.
Discrete random variables. Standard discrete distributions (degenerate, Bernoulli, binomial, discrete uniform, hypergeometric, Poisson, geometric, negative binomial, etc.).
Continuous random variables. Standard continuous distributions (uniform, exponential, gamma, beta, normal, Cauchy, Pareto, etc.).
Introduction to cumulative distribution functions and their properties.
Functions of random variables , expectation/mean , moments, variance, computations of mean using indicator random variables.
Introduction to joint distributions (if time permits).
References:
S. Ross: A First Course in Probability (9th Edition)
W. Feller: Introduction to Probability: Theory and Applications - Vol. I and II
P. G. Hoel, S. C. Port and C. J. Stone: Introduction to Probability Theory
Class Timing:
Wed and Fri, 10:00 AM - 11:00 AM, 11:15 AM - 12:15 PM
Lectures will be held in G24. Students should attend classes regularly and take notes for better understanding. Lecture notes will be uploaded here from time to time.
Problems:
Problems will be given regularly in the lectures. The students will not have to submit the solutions. However, they are encouraged to solve them all, discuss the solutions with each other and also ask the teacher if there is any doubt. Problems similar to these will be given in the exams.
Method of Evaluation:
Evaluation will be carried out based on a mid-semester examination and a final examination with 50% weightage on each.