Learn · Introduction to Probability Theory and Stochastic Processes
Lecture 11 of 92Week 2
Distribution of Function of Random Variables
Prof. S Dharmaraja · IIT Delhi
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- Introduction to Probability Theory and Stochastic Processes, IIT Delhi (at NPTEL)
- Licence
- CC BY-NC-SA, as NPTEL states it. Non-commercial use only.
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- NPTEL states: "Distributed under Creative Commons Attribution-ShareAlike / CC BY - NC - SA", beside a BY-NC-SA badge.
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All the lectures
- Random experiment, sample space, axioms of probability, probability space
- Random experiment, sample space, axioms of probability, probability space. (Cont...)
- Random experiment, sample space, axioms of probability, probability space. (Contd...)
- Conditional probability, independence of events.
- Multiplication rule, total probability rule, Bayes's theorem.
- Definition of Random Variable, Cumulative Distribution Function
- Definition of Random Variable, Cumulative Distribution Function (Continued 1)
- Definition of Random Variable, Cumulative Distribution Function (Continued 2)
- Type of Random Variables, Probability Mass Function, Probability Density Function
- Type of Random Variables, Probability Mass Function, Probability Density Function (continued 1)
- Distribution of Function of Random Variables
- Mean and Variance
- Mean and Variance Continued
- Higher Order Moments and Moments Inequalities
- Higher Order Moments and Moments Inequalities Continued
- Generating Functions
- Generating Functions Continued
- Common Discrete Distributions
- Common Discrete Distributions Continued
- Common Continuous Distributions
- Common Continuous Distributions Continued
- Applications of Random Variable
- Applications of Random Variable Continued
- Random vector and joint distribution
- Joint probability mass function
- Joint probability density function
- Independent random variables
- Independent random variables Continued
- Functions of several random variables
- Functions of several random variables continued
- Some important results
- Order statistics
- Conditional distributions
- Random sum
- Moments and Covariance
- Variance Covariance matrix
- Multivariate Normal distribution
- Probability generating function and Moment generating function
- Correlation coefficient
- Conditional Expectation
- Conditional Expectation continued
- Modes of Convergence
- Mode of Convergence (Continued)
- Law of Large Numbers
- Central Limit Theorem
- Central Limit Theorem (Continued)
- Motivation for Stochastic Processes
- Definition of a Stochastic Process
- Classification of Stochastic Processes
- Examples of Stochastic Process
- Examples Of Stochastic Process (Continued)
- Bernoulli Process
- Poisson Process
- Poisson Process (Continued)
- Simple Random Walk
- Time Series and Related Definitions
- Strict Sense Stationary Process
- Wide Sense Stationary Process and Examples
- Examples of Stationary Processes Continued
- Discrete Time Markov Chain (DTMC)
- DTMC continued
- Examples of DTMC
- Examples of DTMC continued
- Chapman-Kolmogorov equations and N-step transition matrix
- Examples based on N-step transition matrix
- Examples continued
- Classification of states
- Classification of states continued
- Calculation of N-Step-9
- Calculation of N-Step-10
- Limiting and Stationary distributions
- Limiting and Stationary distributions continued
- Continuous time Markov chain (CTMC)
- CTMC continued
- State transition diagram and Chapman-Kolmogorov equation
- Infinitesimal generator and Kolmogorov differential equations
- Limiting distribution
- Limiting and Stationary distributions -1
- Birth death process
- Birth death process continued
- Poisson process -1
- Poisson process continued
- Poisson process (cont.)
- Non-homogeneous and compound Poisson process
- Introduction to Queueing Models and Kendall Notation
- M/M/1 Queueing Model
- M/M/1 Queueing Model Continued...
- M/M/1 Queueing Model and Burke's Theorem
- M/M/c Queueing Model
- M/M/c continued and M/M/1/N Model
- Other Markovian Queueing Models
- Transient Solution of Finite Capacity Markovian Queues