Mathematics - iii (Differential Calculus) - Vol 3 | 13. Probability Density Function (pdf) by Abraham | Learn Smarter
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13. Probability Density Function (pdf)

13. Probability Density Function (pdf)

Probability Density Functions (PDFs) are essential in the context of continuous random variables. They describe the distribution of values along with their properties, enabling the calculation of probabilities and statistical modeling. Key applications of PDFs span various fields, including engineering and data science, where they help analyze random phenomena effectively.

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  1. 13.
    Partial Differential Equations

    This section introduces the concept of Probability Density Functions (PDFs),...

  2. 13.1
    Probability Density Function (Pdf)

    The Probability Density Function (PDF) describes the distribution of...

  3. 13.1.1
    Random Variables: Discrete Vs Continuous

    The section discusses the fundamental concepts of random variables,...

  4. 13.1.2
    What Is A Probability Density Function (Pdf)?

    The Probability Density Function (PDF) describes the distribution of...

  5. 13.1.3
    Properties Of Pdf

    This section discusses the crucial properties of Probability Density...

  6. 13.1.4
    Cumulative Distribution Function (Cdf)

    The Cumulative Distribution Function (CDF) describes the probability that a...

  7. 13.1.5
    Common Probability Density Functions

    Probability Density Functions (PDFs) are critical for understanding...

  8. 13.1.6
    Mean And Variance Using Pdf

    This section focuses on calculating the mean and variance of continuous...

  9. 13.1.7
    Solved Examples

    In this section, we explore solved examples related to Probability Density...

  10. 13.1.8
    Applications Of Pdf In Engineering

    This section discusses the applications of Probability Density Functions...

What we have learnt

  • A Probability Density Function (PDF) defines the distribution of continuous random variables.
  • The properties of PDFs include non-negativity and the requirement that the total area under the curve equals one.
  • Probability is calculated over intervals, and the expected value and variance can be deduced from PDFs.

Key Concepts

-- Probability Density Function (PDF)
A function that describes the likelihood of a continuous random variable taking on a particular value.
-- Cumulative Distribution Function (CDF)
A function that provides the probability that a random variable is less than or equal to a certain value.
-- Expected Value
The average value of a random variable calculated from its probability density function.
-- Variance
A measure of the dispersion of a set of values; it indicates how far the values are spread out from the mean.

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