Probability Theory and Applications


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