Unit 1: Basic Prbablity
- Introduction to the notion of probability
- Random experiment
- Sample space and Events
- Probability defined on events
- Algebra of events
- Conditional probabilities
- Independent events
- Bayes’ theorem
Unit 2: Random Variables
- Introduction to Random Variables
- Probability mass/density functions
- Cumulative distribution functions
- Discrete Random Variables (Bernoulli, Binomial, Poisson, Multinomial and Geometric)
- Continuous Random Variables (Uniform, Exponential and Normal)
- Expectation of a Random Variable
- Expectation of Function of a Random Variable and Variance
- Markov inequality
- Chebyshev’s inequality
- Central Limit Theorem
- Weak and Strong Laws of Large Numbers
Unit 3: Joint Distributions
- Jointly distributed Random Variables
- Joint distribution functions
- Independent Random Variables
- Covariance of Random Variables
- Correlation Coefficients
- Conditional Expectation
Unit 4: Markov Chain and Information Theory
- Introductionn to stochastic processes
- Chapman–Kolmogorov equations
- Classification of states
- Limiting and Stationary Probabilities
- Random Number Generation
- Pseudo Random Numbers
- Inverse Transformation Method
- Rejection Method
- Uncertainty
- Information and Entropy
- Mutual Information
- KL Divergence
