Mathematics - iii (Differential Calculus) - Vol 3 | 18. Binomial Distribution by Abraham | Learn Smarter
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18. Binomial Distribution

The Binomial Distribution is a crucial discrete probability distribution modeling the number of successes in fixed independent Bernoulli trials. It operates under specific assumptions and includes key statistical measures such as mean, variance, and standard deviation, among others. The distribution is widely applied across various fields including engineering, quality control, and finance, and can be approximated by a normal distribution under certain conditions.

Sections

  • 18

    Partial Differential Equations

    The Binomial Distribution models the number of successes in a fixed number of Bernoulli trials, characterized by several key properties and applications.

    Learning Practice

  • 18.X

    Binomial Distribution – Complete Detail

    The Binomial Distribution models the probability of obtaining a specific number of successes in a fixed number of independent Bernoulli trials.

    Learning Practice

  • 18.X.1

    Definition

    The Binomial Distribution quantifies the probability of achieving exactly k successes in n independent Bernoulli trials.

    Learning Practice

  • 18.X.2

    Assumptions Of Binomial Distribution

    The assumptions of the binomial distribution outline the necessary conditions for modeling situations involving a fixed number of independent trials with binary outcomes.

    Learning Practice

  • 18.X.3

    Properties Of Binomial Distribution

    This section covers the essential properties of the Binomial Distribution, including its mean, variance, standard deviation, skewness, and kurtosis.

    Learning Practice

  • 18.X.4

    Examples

    This section provides practical examples of calculating probabilities using the Binomial Distribution.

    Learning Practice

  • 18.X.5

    Cumulative Distribution Function (Cdf)

    The Cumulative Distribution Function (CDF) gives the probability of obtaining at most k successes in a binomial distribution.

    Learning Practice

  • 18.X.6

    Real-World Applications

    The section discusses the diverse real-world applications of the Binomial Distribution in various fields such as engineering, biology, and finance.

    Learning Practice

  • 18X.7

    Approximation To Normal Distribution

    This section discusses how the binomial distribution can be approximated by the normal distribution under certain conditions.

    Learning Practice

  • 18.X.8

    Relation To Pdes (Advanced Insight)

    The Binomial Distribution, while not directly related to solving Partial Differential Equations (PDEs), influences stochastic processes and numerical simulations that use PDEs.

    Learning Practice

References

unit 3 ch18.pdf

Class Notes

Memorization

What we have learnt

  • The Binomial Distribution d...
  • It requires that trials be ...
  • Essential characteristics i...

Final Test

Revision Tests