School of Computer Engineeringcoretheory
PROBABILITY AND OPTIMIZATION
MAT 2201
Syllabus
- 01Axioms of probability
- 02Baye's theorem - Applications
- 03One dimensional and Two-dimensional random variables
- 04mean and variance
- 05properties
- 06Chebyshev's inequality
- 07Correlation Coefficient
- 08Markov Chains
- 09Distributions: Discrete and Continuous
- 10Binomial
- 11Poisson
- 12exponential
- 13Normal and Chi-square
- 14Moment generating function
- 15properties
- 16Functions of random variables - One-Two dimensional
- 17Jacobians
- 18Sampling theory: Central limit theorem
- 19Point estimation
- 20Maximum Likelihood Estimator
- 21Hypothesis: significance level
- 22Chi square test
- 23Gradients of Matrices: Useful Identities for Computing Gradients
- 24Backpropagation and Automatic Differentiation
- 25Constrained Optimization
References
- P. L. Meyer: Introduction to probability and statistical applications, 2nd edition, 1980, Oxford and IBH Publishing, Delhi
- Miller, Freund and Johnson, Probability and Statistics for Engineers, 8th edn., PHI, 2011
- Hogg and Craig, Introduction to Mathematical Statistics, 6th edn, 2012, Pearson Education, New Delhi
- Sheldon M. Ross, Introduction to Probability and Statistics for Engineers and Scientists, Elsevier, 2010
- Marc Peter Deisenroth, A. Aldo Faisal, Cheng Soon Ong, Mathematics for Machine Learning, Cambridge University Press, 2020
- J. Medhi, Stochastic Processes, Third Edition, New Age International, 2009
Credits Structure
3Lecture
0Tutorial
0Practical
3Total