NOC:Probability Theory for Data Science

Lecture 1 - Introduction

Lecture 2 - Sample Space and Events

Lecture 3 - Special Events and Various Approaches to Defining Probability

Lecture 4 - Important Theorems

Lecture 5 - Numerical Examples and Introduction to Conditional Probability

Lecture 6 - Definition of Conditional Probability and Independence

Lecture 7 - Bayes' Theorem

Lecture 8 - Random Variable

Lecture 9 - Events Defined by a Random Variable

Lecture 10 - Cumulative Distribution Function

Lecture 11 - Properties of the Cumulative Distribution Function and Discrete Random Variable

Lecture 12 - Probability Mass Function

Lecture 13 - Continuous Random Variable and Probability Density Function

Lecture 14 - Numerical Examples

Lecture 15 - Moments

Lecture 16 - Higher Order Moments and Variance of a Random Variable

Lecture 17 - Numerical Examples of Moments and Bernoulli Distribution

Lecture 18 - Binomial Distribution

Lecture 19 - Applications of Binomial Distribution

Lecture 20 - Poisson Distribution

Lecture 21 - Applications of Poisson Distribution

Lecture 22 - Numerical Examples of Poisson Distribution and Uniform Distribution

Lecture 23 - Application of Uniform Distribution and Exponential Distribution

Lecture 24 - Applications of Exponential Distribution

Lecture 25 - Memoryless Property and Gamma Distribution

Lecture 26 - Example of Gamma Distribution and Normal Distribution

Lecture 27 - Properties of Normal Distributions

Lecture 28 - Numerical Examples of Normal Distributions

Lecture 29 - Applications of Normal Distributions and Conditional Distribution Function

Lecture 30 - Examples of Conditional Distribution Function and Bivariate Random Variable

Lecture 31 - Example of Bivariate Random Variable

Lecture 32 - Properties of the Joint Cumulative Distribution Function of a Bivariate Random Variable

Lecture 33 - Independence Between Two Random Variables

Lecture 34 - Examples of Joint Cumulative Distribution Functions, Marginals, and Independence

Lecture 35 - Joint Probability Mass Function, Marginal Probability Mass Function, Examples

Lecture 36 - Numerical Examples on Bivariate Discrete Random Variables and the Concept of Joint Probability

Lecture 37 - Marginal Probability Density Function, Independence, and Examples

Lecture 38 - Numerical Examples on Probability Density Function

Lecture 39 - Conditional Probability Mass Function

Lecture 40 - Conditional Probability Density Function

Lecture 41 - Moments for Bivariate Random Variables

Lecture 42 - Association Between Two Random Variables

Lecture 43 - Numerical Examples on Moments for Bivariate Random Variables

Lecture 44 - Conditional Mean and Variance for Discrete Random Variables

Lecture 45 - Conditional Mean and Variance for Continuous Random Variables

Lecture 46 - Numerical Examples on Conditional Mean and Variance

Lecture 47 - Multivariate Random Variables

Lecture 48 - Multivariate Probability Density Function and Independence

Lecture 49 - Moments of a Multivariate Random Variable

Lecture 50 - Numerical Examples on Joint Probability Mass Functions

Lecture 51 - Numerical Examples on Joint Probability Density Functions

Lecture 52 - Multinomial Distribution and Multivariate Normal Distribution

Lecture 53 - Transformation of Random Variables

Lecture 54 - Theorem on Transformation of Random Variables

Lecture 55 - Transformation of Multivariate Random Variables

Lecture 56 - Examples of Transformation of Bivariate Random Variables

Lecture 57 - Convolution and Example on Transformation of n-variate Random Variables

Lecture 58 - Transformation of Discrete Random Variables

Lecture 59 - Moment Generating Functions

Lecture 60 - Example of Moment Generating Functions

Lecture 61 - Moment Generating Functions for the Transformation of Random Variables

Lecture 62 - Chebyshev's Inequality

Lecture 63 - Notions of Convergence, Law of Large Numbers, and the Central Limit Theorem