Mathematics - iii (Differential Calculus) - Vol 3 | 15. Marginal Distributions by Abraham | Learn Smarter
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15. Marginal Distributions

Marginal distributions are vital in understanding individual variables within multivariable distributions. They are created by integrating or summing over other variables, enabling focus on specific probabilities in various applications, especially in engineering fields. The chapter presents the necessary mathematical foundations and practical implications of marginal distributions, emphasizing their importance in multivariate analysis.

Sections

  • 15

    Partial Differential Equations

    This section introduces marginal distributions, emphasizing their significance in analyzing individual random variables within joint probability distributions.

    Learning Practice

  • 15.1

    Concept Of Joint Probability Distributions

    The concept of joint probability distributions introduces the idea of understanding the relationship between multiple random variables through their joint probability density functions.

    Learning Practice

  • 15.2

    Definition Of Marginal Distributions

    Marginal distributions provide insights into individual probability distributions of random variables, removed from the influence of others.

    Learning Practice

  • 15.3

    Discrete Case

    The discrete case of marginal distributions focuses on the probability mass functions of individual random variables derived from their joint distribution.

    Learning Practice

  • 15.4

    Interpretation

    Marginal distributions provide insight into the behavior of individual variables within a joint probability framework, ignoring other variables.

    Learning Practice

  • 15.5

    Applications In Engineering

    This section explores the critical applications of marginal distributions across various engineering fields.

    Learning Practice

  • 15.6

    Worked Example (Continuous Case)

    This section presents a worked example of finding marginal distributions for continuous random variables.

    Learning Practice

  • 15.7

    Properties Of Marginal Distributions

    Marginal distributions are probability distributions of individual variables derived from joint distributions, crucial for understanding variable behaviors independently.

    Learning Practice

  • 15.8

    Independence And Marginals

    This section discusses the concept of independence in joint probability distributions and its relationship with marginal distributions.

    Learning Practice

  • 15.9

    Extension To More Than Two Variables

    This section explores how marginal distributions can be extended to three or more random variables, emphasizing the concept of marginalizing each variable using integration.

    Learning Practice

References

unit 3 ch15.pdf

Class Notes

Memorization

What we have learnt

  • Marginal distributions prov...
  • They are derived by integra...
  • In engineering, marginal di...

Revision Tests