Introduction to Probability Theory and Stochastic Processes HVS7Q39EDW

URI	`m2://res/HVS7Q39EDW`
Kind	course
Creators	S Dharmaraja (instructor)
Date	2018-07-15
MSC	60-XX
Scope	in
Ids	course 049tgcd06:111102111

Expressions

e1: edition

Language	en
Date	2018-07-15

m1: page, IIT Delhi (record). nptel 111102111
m2: page, 2018-07-15 (record). nptel 111102111

Contents

part 1: Week 1
session 1: Random experiment, sample space, axioms of probability, probability space
session 2: Random experiment, sample space, axioms of probability, probability space. (Cont...)
session 3: Random experiment, sample space, axioms of probability, probability space. (Contd...)
session 4: Conditional probability, independence of events.
session 5: Multiplication rule, total probability rule, Bayes's theorem.
part 2: Week 2
session 6: Definition of Random Variable, Cumulative Distribution Function
session 7: Definition of Random Variable, Cumulative Distribution Function (Continued 1)
session 8: Definition of Random Variable, Cumulative Distribution Function (Continued 2)
session 9: Type of Random Variables, Probability Mass Function, Probability Density Function
session 10: Type of Random Variables, Probability Mass Function, Probability Density Function (continued 1)
session 11: Distribution of Function of Random Variables
part 3: Week 3
session 12: Mean and Variance
session 13: Mean and Variance Continued
session 14: Higher Order Moments and Moments Inequalities
session 15: Higher Order Moments and Moments Inequalities Continued
session 16: Generating Functions
session 17: Generating Functions Continued
part 4: Week 4
session 18: Common Discrete Distributions
session 19: Common Discrete Distributions Continued
session 20: Common Continuous Distributions
session 21: Common Continuous Distributions Continued
session 22: Applications of Random Variable
session 23: Applications of Random Variable Continued
part 5: Week 5
session 24: Random vector and joint distribution
session 25: Joint probability mass function
session 26: Joint probability density function
session 27: Independent random variables
session 28: Independent random variables Continued
part 6: Week 6
session 29: Functions of several random variables
session 30: Functions of several random variables continued
session 31: Some important results
session 32: Order statistics
session 33: Conditional distributions
session 34: Random sum
part 7: Week 7
session 35: Moments and Covariance
session 36: Variance Covariance matrix
session 37: Multivariate Normal distribution
session 38: Probability generating function and Moment generating function
session 39: Correlation coefficient
session 40: Conditional Expectation
session 41: Conditional Expectation continued
part 8: Week 8
session 42: Modes of Convergence
session 43: Mode of Convergence (Continued)
session 44: Law of Large Numbers
session 45: Central Limit Theorem
session 46: Central Limit Theorem (Continued)
part 9: Week 9
session 47: Motivation for Stochastic Processes
session 48: Definition of a Stochastic Process
session 49: Classification of Stochastic Processes
session 50: Examples of Stochastic Process
session 51: Examples Of Stochastic Process (Continued)
session 52: Bernoulli Process
session 53: Poisson Process
session 54: Poisson Process (Continued)
session 55: Simple Random Walk
session 56: Time Series and Related Definitions
session 57: Strict Sense Stationary Process
session 58: Wide Sense Stationary Process and Examples
session 59: Examples of Stationary Processes Continued
part 10: Week 10
session 60: Discrete Time Markov Chain (DTMC)
session 61: DTMC continued
session 62: Examples of DTMC
session 63: Examples of DTMC continued
session 64: Chapman-Kolmogorov equations and N-step transition matrix
session 65: Examples based on N-step transition matrix
session 66: Examples continued
session 67: Classification of states
session 68: Classification of states continued
session 69: Calculation of N-Step-9
session 70: Calculation of N-Step-10
session 71: Limiting and Stationary distributions
session 72: Limiting and Stationary distributions continued
part 11: Week 11
session 73: Continuous time Markov chain (CTMC)
session 74: CTMC continued
session 75: State transition diagram and Chapman-Kolmogorov equation
session 76: Infinitesimal generator and Kolmogorov differential equations
session 77: Limiting distribution
session 78: Limiting and Stationary distributions -1
session 79: Birth death process
session 80: Birth death process continued
session 81: Poisson process -1
session 82: Poisson process continued
session 83: Poisson process (cont.)
session 84: Non-homogeneous and compound Poisson process
part 12: Week 12
session 85: Introduction to Queueing Models and Kendall Notation
session 86: M/M/1 Queueing Model
session 87: M/M/1 Queueing Model Continued...
session 88: M/M/1 Queueing Model and Burke's Theorem
session 89: M/M/c Queueing Model
session 90: M/M/c continued and M/M/1/N Model
session 91: Other Markovian Queueing Models
session 92: Transient Solution of Finite Capacity Markovian Queues

Catalogue records

nptel: 111102111 (manifestation)
nptel_video: 111102111 (manifestation)