Instructor : Prof. Kaushik Saha
Course Description :
- A prerequisite for all the statistic minor courses.
- Quiz 1: 10%; Quiz 2: 10%; Midsem: 30% and Endsem: 50%
- Manual attendance taken during class ( runs in minor slot ). Tutorial is conducted every week.
- Syllabus : Sample spaces, events, sigma algebra, probability space, properties of probabilities, conditional probability, independence, Bayes formula, Polya’s urn model, some combinatorial problems, Discrete random variables, probability mass function, independent random variable, sum of random variables, random vector, expectation of discrete random variable, properties of expectation and variance, Continuous random variable, distribution function, density of a continuous random variable, expectation, change of variable formula, random vector, joint distribution of random variables, joint density, distribution of sums and products of random variables, conditional density, conditional expectation, order statistics, moment generating function, characteristic function, Inequalities: Markov, Chebyshev, one sided chebyshev, Schwarz and Chernoff bound, Almost sure convergence, strong law large number (SLLN), convergence in probability, weak law of large number (WLLN), convergence in distribution, central limit theorem(CLT). Relation between three mode of convergence
References :
- Introduction to probability models, by Sheldon Ross.
- Introduction to probability theory, by Hoel, Port and Stone.
Comments on Instructor :
- Instructor is friendly and is interested in students learning and understanding of the course content.
Comments on course :
- It is very important to maintain good lecture notes ( no slides are provided). This will be of great help during exams for this course.
- Typically the lecture notes are complete and understanding them is enough to perform well in this course with a bit of practice before the exams.
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