Mathematics - iii (Differential Calculus) - Vol 3 | 12. Probability Mass Function (PMF) by Abraham | Learn Smarter
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Knowledge
12. Probability Mass Function (PMF)

The Probability Mass Function (PMF) is a fundamental concept in probability theory that describes the distribution of a discrete random variable. It assigns probabilities to distinct outcomes and is essential for modeling uncertainty in various fields, particularly in engineering and data science. PMFs are vital for calculating expected values and variances, paving the way for more complex probabilistic models used in applications like partial differential equations and stochastic modeling.

Sections

  • 12

    Partial Differential Equations

    The section explores Probability Mass Function (PMF), essential for modeling discrete random variables in fields like telecommunications and machine learning.

    Learning Practice

  • 12.1

    What Is A Discrete Random Variable?

    This section introduces the concept of discrete random variables and highlights the significance of the Probability Mass Function (PMF) in understanding their distribution.

    Learning Practice

  • 12.2

    Definition Of Probability Mass Function (Pmf)

    The Probability Mass Function (PMF) describes the probability distribution of a discrete random variable, mapping each possible outcome to its likelihood.

    Learning Practice

  • 12.3

    Properties Of Pmf

    This section discusses the essential properties of the Probability Mass Function (PMF), including non-negativity, normalization, and the requirement of a discrete domain.

    Learning Practice

  • 12.4

    Example Of Pmf

    This section illustrates the Probability Mass Function (PMF) through practical examples, specifically focusing on a fair coin toss and a fair die roll.

    Learning Practice

  • 12.5

    Graphical Representation Of Pmf

    This section focuses on how to visually represent the Probability Mass Function (PMF) through graphical means like bar graphs.

    Learning Practice

  • 12.6

    Cumulative Distribution Function (Cdf) Vs Pmf

    This section contrasts the Probability Mass Function (PMF) and the Cumulative Distribution Function (CDF), highlighting their definitions and interrelationships.

    Learning Practice

  • 12.7

    Applications Of Pmf In Engineering

    This section explores the various applications of Probability Mass Function (PMF) in engineering fields.

    Learning Practice

  • 12.8

    Pmf Vs Pdf Vs Cdf

    This section explores the differences and definitions of the Probability Mass Function (PMF), Probability Density Function (PDF), and Cumulative Distribution Function (CDF).

    Learning Practice

  • 12.9

    Common Discrete Distributions And Their Pmfs

    This section explores common discrete distributions and their Probability Mass Functions (PMFs), highlighting their definitions and characteristics.

    Learning Practice

  • 12.10

    Important Points To Remember

    The PMF is crucial for understanding probabilities associated with discrete random variables and helps in real-world applications.

    Learning Practice

References

unit 3 ch12.pdf

Class Notes

Memorization

What we have learnt

  • The PMF provides a clear de...
  • A valid PMF must satisfy pr...
  • PMFs are crucial in various...

Final Test

Revision Tests