Probability Theory for Data Science KRBKT0SBPR

URI	`m2://res/KRBKT0SBPR`
Kind	course
Creators	Ishapathik Das (instructor)
Date	2025-03-18
Scope	in

Expressions

e1: edition

Language	en
Date	2025-03-18

m1: page, IIT Tirupati (record). nptel 111106525
m2: page, 2025-03-18 (record). nptel 111106525

Contents

part 1: Week 1
session 1: Introduction
session 2: Sample Space and Events
session 3: Special Events and Various Approaches to Defining Probability
session 4: Important Theorems
session 5: Numerical Examples and Introduction to Conditional Probability
session 6: Definition of Conditional Probability and Independence
part 2: Week 2
session 7: Bayes' Theorem
session 8: Random Variable
session 9: Events Defined by a Random Variable
session 10: Cumulative Distribution Function
part 3: Week 3
session 11: Properties of the Cumulative Distribution Function and Discrete Random Variable
session 12: Probability Mass Function
session 13: Continuous Random Variable and Probability Density Function
session 14: Numerical Examples
session 15: Moments
part 4: Week 4
session 16: Higher Order Moments and Variance of a Random Variable
session 17: Numerical Examples of Moments and Bernoulli Distribution
session 18: Binomial Distribution
session 19: Applications of Binomial Distribution
session 20: Poisson Distribution
part 5: Week 5
session 21: Applications of Poisson Distribution
session 22: Numerical Examples of Poisson Distribution and Uniform Distribution
session 23: Application of Uniform Distribution and Exponential Distribution
session 24: Applications of Exponential Distribution
session 25: Memoryless Property and Gamma Distributio
part 6: Week 6
session 26: Example of Gamma Distribution and Normal Distribution
session 27: Properties of Normal Distributions
session 28: Numerical Examples of Normal Distributions
session 29: Applications of Normal Distributions and Conditional Distribution Function
session 30: Examples of Conditional Distribution Function and Bivariate Random Variable
session 31: Example of Bivariate Random Variable
part 7: Week 7
session 32: Properties of the Joint Cumulative Distribution Function of a Bivariate Random Variable
session 33: Independence Between Two Random Variables
session 34: Examples of Joint Cumulative Distribution Functions, Marginals, and Independence
session 35: Joint Probability Mass Function, Marginal Probability Mass Function, Examples
session 36: Numerical Examples on Bivariate Discrete Random Variables and the Concept of Joint Probability Density Function
session 37: Marginal Probability Density Function, Independence, and Examples
part 8: Week 8
session 38: Numerical Examples on Probability Density Function
session 39: Conditional Probability Mass Function
session 40: Conditional Probability Density Function
session 41: Moments for Bivariate Random Variables
session 42: Association Between Two Random Variables
part 9: Week 9
session 43: Numerical Examples on Moments for Bivariate Random Variables
session 44: Conditional Mean and Variance for Discrete Random Variables
session 45: Conditional Mean and Variance for Continuous Random Variables
session 46: Numerical Examples on Conditional Mean and Variance
session 47: Multivariate Random Variables
part 10: Week 10
session 48: Multivariate Probability Density Function and Independence
session 49: Moments of a Multivariate Random Variable
session 50: Numerical Examples on Joint Probability Mass Functions
session 51: Numerical Examples on Joint Probability Density Functions
session 52: Multinomial Distribution and Multivariate Normal Distribution
part 11: Week 11
session 53: Transformation of Random Variables
session 54: Theorem on Transformation of Random Variables
session 55: Transformation of Multivariate Random Variables
session 56: Examples of Transformation of Bivariate Random Variables
session 57: Convolution and Example on Transformation of n-variate Random Variables
part 12: Week 12
session 58: Transformation of Discrete Random Variables
session 59: Moment Generating Functions
session 60: Example of Moment Generating Functions
session 61: Moment Generating Functions for the Transformation of Random Variables
session 62: Chebyshev's Inequality
session 63: Notions of Convergence, Law of Large Numbers, and the Central Limit Theorem

Catalogue records

nptel: 111106525 (manifestation)
nptel_video: 111106525 (manifestation)