IIT Kanpur Course , Prof. Prabha Sharma

**105**students enrolled

IIT Kanpur Course , Prof. Prabha Sharma

Basic principles of counting - Sample space , events, axioms of probability - Conditional probability, Independence of events - Random variables, cumulative density function, expected value - Discrete random variables and their distributions - Continuous random variables and their distributions - Function of random variables, Momement generating function - Jointly distributed random variables, Independent r. v. and their sums - Independent r. v. and their sums - Chi square r. v., sums of independent normal r. v., Conditional distr - Conditional distributions, Joint distr. of functions of r. v., Order statistics - Order statistics, Covariance and correlation - Covariance, Correlation, Cauchy- Schwarz inequalities, Conditional expectation - Conditional expectation, Best linear predictor - Inequalities and bounds - Convergence and limit theorems - Central limit theorem

Applications of central limit theorem - Strong law of large numbers, Joint mgf - Convolutions - Stochastic processes: Markov process - Transition and state probabilities - State prob., First passage and First return prob - First passage and First return prob. Classification of states - Random walk, periodic and null states - Reducible Markov chains - Time reversible Markov chains - Poisson Processes - Inter-arrival times, Properties of Poisson processes - Queuing Models: M/M/I, Birth and death process, Littles formulae - Analysis of L, Lq ,W and Wq , M/M/S model - M/M/S , M/M/I/K models - M/M/I/K and M/M/S/K models - Application to reliability theory failure law - Exponential failure law, Weibull law - Reliability of systems

Applications of central limit theorem - Strong law of large numbers, Joint mgf - Convolutions - Stochastic processes: Markov process - Transition and state probabilities - State prob., First passage and First return prob - First passage and First return prob. Classification of states - Random walk, periodic and null states - Reducible Markov chains - Time reversible Markov chains - Poisson Processes - Inter-arrival times, Properties of Poisson processes - Queuing Models: M/M/I, Birth and death process, Littles formulae - Analysis of L, Lq ,W and Wq , M/M/S model - M/M/S , M/M/I/K models - M/M/I/K and M/M/S/K models - Application to reliability theory failure law - Exponential failure law, Weibull law - Reliability of systems

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3.4 (29 Ratings)

Probability Theory and Applications by Prof. Prabha Sharma,Department of Mathematics,IIT Kanpur.For more details on NPTEL visit httpnptel.ac.in.

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

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