CMI, Jan-Apr 2025, R Srinivasan
Hoel et al. (1996), Lecture recordings
Lecture notes
- LEC PROB 1 ✅
- Probability spaces, some properties of the probability measure
- LEC PROB 2 ✅
- More properties of the probability measure, Conditional probability
- LEC PROB 3 ✅
- Independent events, discrete random variables, binomial distribution, the distribution function
- LEC PROB 4 ✅
- Examples of probability mass distributions: Geometric, hypergeometric, negative binomial, poisson
- LEC PROB 5 ✅
- Random vectors, independent random variables
- LEC PROB 6
- Infinite sequences of Bernoulli trials, Sums of independent random variables, The probability generating function
- LEC PROB 7
- Expectation: Properties of expectation, moments, variance, correlation coefficient, Schwarz inequality, Chebyshev’s inequality, Weak and Strong laws of large numbers, conditional expectation
- LEC PROB 8 ✅
- Continuous random variables, symmetric, uniform, normal, exponential, and gamma densities.
- LEC PROB 9 ✅
- Expectation and moments of continuous random variables
- LEC PROB 10 ✅
- Distributions of sums and quotients, Characteristic functions
- LEC PROB 11
Quizzes
TST PROB Quiz 1
TST PROB Quiz 3
Assignments
AS PROB 1
TST PROB MidsemPartB
AS PROB ClassAssignment
AS PROB 2
References
Hoel, P. G., Port, S. C., & Stone, C. J. (1996). Introduction to Probability Theory (Nachdr.). Houghton Mifflin.