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Probability Theory and Applications. Instructor: Prof. Prabha Sharma, Department of Mathematics and Statistics, IIT Kanpur.
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Description
The aim of this course is to familiarise students with basic concepts of Probability Theory with reasonable amount of rigor. Examples will be used for motivating students to learn and understand the basic concepts. Topics include: basics of probability theory, random variables, moments and other functions of random variables, limit theorems and inequalities, Poisson process, and Markov chains. (from nptel.ac.in)
Course content
- Lecture 01 – Basic Principles of Counting Unlimited
- Lecture 02 – Sample Space, Events, Axioms of Probability Unlimited
- Lecture 03 – Conditional Probability, Independence of Events Unlimited
- Lecture 04 – Random Variables, Cumulative Density Function, Expected Value Unlimited
- Lecture 05 – Discrete Random Variables and their Distributions Unlimited
- Lecture 06 – Discrete Random Variables and their Distributions (cont.) Unlimited
- Lecture 07 – Discrete Random Variables and their Distributions (cont.) Unlimited
- Lecture 08 – Continuous Random Variables and their Distributions Unlimited
- Lecture 09 – Continuous Random Variables and their Distributions (cont.) Unlimited
- Lecture 10 – Continuous Random Variables and their Distributions (cont.) Unlimited
- Lecture 11 – Function of Random Variables, Moment Generating Function Unlimited
- Lecture 12 – Jointly Distributed Random Variables, Independent Random Variables and their Sums Unlimited
- Lecture 13 – Independent Random Variables and their Sums Unlimited
- Lecture 14 – Chi-Square Random Variables, Sums of Independent Normal Random Variables Unlimited
- Lecture 15 – Conditional Distribution, Joint Distribution of Functions of Random Variables Unlimited
- Lecture 16 – Order statistics, Covariance and Correlation Unlimited
- Lecture 17 – Covariance, Correlation, Cauchy-Schwarz Inequalities, Conditional Expectation Unlimited
- Lecture 18 – Conditional Expectation, Best Predictor Unlimited
- Lecture 19 – Inequalities and Bounds Unlimited
- Lecture 20 – Convergence and Limit Theorem Unlimited
- Lecture 21 – Central Limit Theorem Unlimited
- Lecture 22 – Applications of Central Limit Theorem Unlimited
- Lecture 23 – Strong Law of Large Numbers, Joint Moment Generating Function Unlimited
- Lecture 24 – Convolutions Unlimited
- Lecture 25 – Stochastic Processes: Markov Process Unlimited
- Lecture 26 – Transition and State Probabilities Unlimited
- Lecture 27 – Steady State Probabilities, First Passage and First Return Probabilities Unlimited
- Lecture 28 – First Passage and First Return Probabilities, Classification of States Unlimited
- Lecture 29 – Random Walk, Periodic and Null States Unlimited
- Lecture 30 – Reducible Markov Chains Unlimited
- Lecture 31 – Time Reversible Markov Chains Unlimited
- Lecture 32 – Poisson Processes Unlimited
- Lecture 33 – Inter-Arrival Times, Properties of Poisson Processes Unlimited
- Lecture 34 – Queuing Models: M/M/1, Birth and Death Process, Little’s Formulae Unlimited
- Lecture 35 – Analysis of L, Lq, W and Wq, M/M/S Model Unlimited
- Lecture 36 – M/M/S , M/M/1/K Models Unlimited
- Lecture 37 – M/M/1/K and M/M/S/K Models Unlimited
- Lecture 38 – Application to Reliability Theory, Failure Law Unlimited
- Lecture 39 – Exponential Failure Law, Weibull Law Unlimited
- Lecture 40 – Reliability of Systems Unlimited
Instructor
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