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Probability Theory and Applications (Video)
Modules / Lectures
Probability Theory and Applications
Lecture-01-Basic principles of counting
Lecture-02-Sample space , events, axioms of probability
Lecture-03-Conditional probability, Independence of events.
Lecture-04-Random variables, cumulative density function, expected value
Lecture-05-Discrete random variables and their distributions
Lecture-06-Discrete random variables and their distributions
Lecture-07-Discrete random variables and their distributions
Lecture-08-Continuous random variables and their distributions.
Lecture-09-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-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-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
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Concepts covered in this lecture :
Basic principles of counting
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