Mathematics - iii (Differential Calculus) - Vol 3 | 14. Joint Probability Distributions by Abraham | Learn Smarter
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14. Joint Probability Distributions

The chapter delves into Joint Probability Distributions, detailing their significance in understanding the relationships between multiple random variables. Various concepts such as marginal distributions, conditional distributions, and independence of random variables are thoroughly explained, providing a foundational understanding for advanced statistical analysis. Additionally, expectation, covariance, and correlation coefficients are discussed to further elucidate the associations between variables.

Sections

  • 14

    Partial Differential Equations

    This section introduces Joint Probability Distributions, which describe the relationship between multiple random variables, critical for fields like statistics and data science.

    Learning Practice

  • 14.1

    Definitions And Basics

    This section provides a foundational understanding of joint probability distributions and the key associated concepts such as random variables and marginal distributions.

    Learning Practice

  • 14.1.1

    Random Variables

    Random variables are functions that assign real numbers to outcomes in a sample space, categorized as discrete or continuous.

    Learning Practice

  • 14.1.2

    Joint Probability Distribution

    Joint Probability Distributions describe the relationship between multiple random variables, allowing the analysis of their combined behavior.

    Learning Practice

  • 14.2

    Properties Of Joint Distributions

    This section covers the foundational properties of joint probability distributions for discrete and continuous random variables, including their definitions and significance.

    Learning Practice

  • 14.2.1

    For Discrete Random Variables

    This section focuses on joint probability distributions for discrete random variables, outlining their core properties and significance in statistical analysis.

    Learning Practice

  • 14.2.2

    For Continuous Random Variables

    This section focuses on the properties and significance of joint probability distributions specifically for continuous random variables.

    Learning Practice

  • 14.3

    Marginal Distributions

    Marginal distributions are used to analyze individual outcomes of joint probability distributions involving multiple random variables.

    Learning Practice

  • 14.3.1

    Marginal Pmf (Discrete)

    Marginal PMF outlines how to derive the marginal probability mass function for discrete random variables from a joint probability distribution.

    Learning Practice

  • 14.3.2

    Marginal Pdf (Continuous)

    Marginal PDFs provide a method to derive the distribution of a single continuous random variable from a joint probability distribution.

    Learning Practice

  • 14.4

    Conditional Distributions

    Conditional distributions describe the distribution of one random variable given a fixed value of another random variable.

    Learning Practice

  • 14.4.1

    Conditional Pmf

    Conditional PMF defines the probability of a random variable given a specific value of another variable.

    Learning Practice

  • 14.4.2

    Conditional Pdf

    The section on Conditional PDF explains how to determine the probability density of a random variable given the value of another variable.

    Learning Practice

  • 14.5

    Independence Of Random Variables

    This section discusses the concept of independence between random variables, outlining the criteria for independence in both discrete and continuous cases.

    Learning Practice

  • 14.6

    Expectation And Covariance

    This section discusses the concepts of expectation and covariance, which are fundamental in understanding the relationships between multiple random variables.

    Learning Practice

  • 14.6.1

    Expectation (Mean)

    Expectation quantifies the average value of a random variable, providing insight into its behavior over time.

    Learning Practice

  • 14.6.2

    Covariance

    Covariance is a measure of how two random variables change together, revealing their relationship and correlation.

    Learning Practice

  • 14.7

    Correlation Coefficient

    The correlation coefficient quantifies the linear relationship between two random variables, indicating how closely they move together.

    Learning Practice

  • 14.8

    Example Problems

    This section presents example problems illustrating the use of joint probability distributions, covering both discrete and continuous cases.

    Learning Practice

References

unit 3 ch14.pdf

Class Notes

Memorization

What we have learnt

  • Joint Probability Distribut...
  • Marginal distributions prov...
  • Independence of random vari...

Final Test

Revision Tests