Learn · Introduction to Probability Theory and Stochastic Processes (Tamil)
Lecture 18 of 53Week 5
Lecture 18 : Definition and Joint Distribution of a Random Vector
Prof. S Dharmaraja · IIT Delhi
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- Introduction to Probability Theory and Stochastic Processes (Tamil), IIT Delhi (at NPTEL)
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All the lectures
- Lecture 1 : Random Experiment, Sample Space and Sigma Field
- Lecture 2 :Axiomatic Definition of Probability
- Lecture 3 : Properties of Axiomatic Definition of Probability and Classical Definition of Probability
- Lecture 4 : Conditional Probability, Independent Events and Baye's Rule
- Lecture 5 : Definition of Random Variable
- Lecture 6 : Cumulative Distribution Function
- Lecture 7 : Discrete and Continuous Type Random Variables
- Lecture 8 : Mixed Type Random Variable
- Lecture 9 : Function of a Random Variable
- Lecture 10 : Mean
- Lecture 11 : Variance and higher order moments
- Lecture 12 : Inequalities of Markov and Chebyshev
- Lecture 13 : Generating functions
- Lecture 14 : Standard discrete distributions
- Lecture 15 : Standard discrete distributions (continued)
- Lecture 16 : Standard continuous distributions
- Lecture 17 : Standard continuous distributions (continued)
- Lecture 18 : Definition and Joint Distribution of a Random Vector
- Lecture 19 : Joint Probability Mass Function
- Lecture 20 : Joint Probability Density Function
- Lecture 21 : Independent Random Vector
- Lecture 22 : Distribution of functions of random variables (Discrete type)
- Lecture 23 : Distribution of functions of random variables (Continuous type)
- Lecture 24 : Conditional Distribution of Random Variables (Discrete type)
- Lecture 25 : Conditional Distribution of Random Variables (Continuous type)
- Lecture 26 : Expectation for several random variables
- Lecture 27 : Covariance and correlation coefficient
- Lecture 28 : Generating functions for several random variables
- Lecture 29 : Conditional Expectation
- Lecture 30 : Modes of convergence
- Lecture 31 : Modes of convergence (contd)
- Lecture 32 : Law of Large Numbers
- Lecture 33 : Central Limit Theorem
- Lecture 34 : Definition and Classification of Stochastic Processes
- Lecture 35 : Properties of Stochastic Processes
- Lecture 36 : Properties of Stochastic Processes(Contd)
- Lecture 37 : Standard Simple Stochastic Processes
- Lecture 38: Definition of Discrete Time Markov Chain (DTMC)
- Lecture 39: Chapman-Kolmogorov Equation
- Lecture 40: Classification of States
- Lecture 41 : Classification of States (Contd)
- Lecture 42 : Limiting Distribution
- Lecture 43 : Stationary Distribution
- Lecture 44 : Reducible Markov Chains
- Lecture 45 : Definition of Continuous Time Markov Chain (CTMC)
- Lecture 46 : Infinitesimal Generator Matrix
- Lecture 47 : Kolmogorov Differential Equations
- Lecture 48 : Limiting Distribution and Steady-State Distribution
- Lecture 49 : Birth Death Processes
- Lecture 50 : Introduction to Queueing Models and Kendall Notation
- Lecture 51 : Single-Server Queueing Models
- Lecture 52 : Single-Server Queueing Models (Contd)
- Lecture 53 : Multi-Server Queueing Models