Probability for Computing

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