# InfoCoBuild

## Probability Theory and Applications

Probability Theory and Applications. Instructor: Prof. Prabha Sharma, Department of Mathematics and Statistics, IIT Kanpur. 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)

 Lecture 34 - Queuing Models: M/M/1, Birth and Death Process, Little's Formulae

Go to the Course Home or watch other lectures:

 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 (cont.) Lecture 07 - Discrete Random Variables and their Distributions (cont.) Lecture 08 - Continuous Random Variables and their Distributions Lecture 09 - Continuous Random Variables and their Distributions (cont.) Lecture 10 - Continuous Random Variables and their Distributions (cont.) Lecture 11 - Function of Random Variables, Moment Generating Function Lecture 12 - Jointly Distributed Random Variables, Independent Random Variables and their Sums Lecture 13 - Independent Random Variables and their Sums Lecture 14 - Chi-Square Random Variables, Sums of Independent Normal R. V., Conditional Distribution Lecture 15 - Conditional Distribution, Joint Distribution of Functions of Random Variables, Order Statistics Lecture 16 - Order statistics, Covariance and Correlation Lecture 17 - Covariance, Correlation, Cauchy-Schwarz Inequalities, Conditional Expectation Lecture 18 - Conditional Expectation, Best Predictor Lecture 19 - Inequalities and Bounds Lecture 20 - Convergence and Limit Theorem Lecture 21 - Central Limit Theorem Lecture 22 - Applications of Central Limit Theorem Lecture 23 - Strong Law of Large Numbers, Joint Moment Generating Function Lecture 24 - Convolutions Lecture 25 - Stochastic Processes: Markov Process Lecture 26 - Transition and State Probabilities Lecture 27 - Steady State Probabilities, First Passage and First Return Probabilities Lecture 28 - First Passage and First Return Probabilities, 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/1, 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/1/K Models Lecture 37 - M/M/1/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