Lecture 1 - Basic principles of counting
Lecture 2 - Sample space, events, axioms of probability
Lecture 3 - Conditional probability, Independence of events
Lecture 4 - Random variables, cumulative density function, expected value
Lecture 5 - Discrete random variables and their distributions
Lecture 6 - Discrete random variables and their distributions
Lecture 7 - Discrete random variables and their distributions
Lecture 8 - Continuous random variables and their distributions
Lecture 9 - Continuous random variables and their distributions
Lecture 10 - Continuous random variables and their distributions
Lecture 11 - Function of random variables, Momement generating function
Lecture 12 - Jointly distributed random variables, Independent r. v. and their sums
Lecture 13 - Independent r. v. and their sums
Lecture 14 - Chi – square r. v., sums of independent normal r. v., Conditional distr
Lecture 15 - Conditional disti, Joint distr. of functions of r. v., Order statistics
Lecture 16 - Order statistics, Covariance and correlation
Lecture 17 - Covariance, Correlation, Cauchy- Schwarz inequalities, Conditional expectation
Lecture 18 - Conditional expectation, Best linear predictor
Lecture 19 - Inequalities and bounds
Lecture 20 - Convergence and limit theorems
Lecture 21 - Central limit theorem
Lecture 22 - Applications of central limit theorem
Lecture 23 - Strong law of large numbers, Joint mgf
Lecture 24 - Convolutions
Lecture 25 - Stochastic processes: Markov process
Lecture 26 - Transition and state probabilities
Lecture 27 - State prob., First passage and First return prob
Lecture 28 - First passage and First return prob. Classification of states
Lecture 29 - Random walk, periodic and null states
Lecture 30 - Reducible Markov chains
Lecture 31 - Time reversible Markov chains
Lecture 32 - Poisson Processes
Lecture 33 - Inter-arrival times, Properties of Poisson processes
Lecture 34 - Queuing Models: M/M/I, Birth and death process, Little’s formulae
Lecture 35 - Analysis of L, Lq ,W and Wq , M/M/S model
Lecture 36 - M/M/S , M/M/I/K models
Lecture 37 - M/M/I/K and M/M/S/K models
Lecture 38 - Application to reliability theory failure law
Lecture 39 - Exponential failure law, Weibull law
Lecture 40 - Reliability of systems
