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Useful for UGC NET · CSIR NET · ASRB NET · ISS

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  1. Welcome
  2. Course Outcomes
  3. Units in this Course
  4. Recommended Textbooks

Welcome

This is the full study package for Theoretical Discrete Distributions. Each of the five units covers one family of discrete distributions in depth — definition, PMF, moments, MGF/CF/CGF/PGF, additive property, skewness, kurtosis, recurrence relations and limiting cases — with two worked examples per concept.

Pre-requisite: Descriptive Statistics and Theory of Probability and Mathematical Expectations. You should be comfortable with PMFs, expectations, MGF and the binomial & exponential series.

Course Outcomes

  1. Deal with data using basic discrete distributions such as Uniform and Binomial.
  2. Acquaint with the Poisson distribution and its applications.
  3. Learn about the Negative Binomial distribution and its real-life applications.
  4. Familiarize with handling data through Geometric and Hypergeometric distributions.

Units in this Course

UNIT 1

Uniform, Bernoulli & Binomial

Discrete uniform; Bernoulli (mean, variance, MGF); Binomial — moments, MGF, CF, CGF, PGF, additive property, skewness, kurtosis, recurrence, normal limit.

 UNIT 2

Poisson Distribution

Definition, moments, MGF, CF, CGF, PGF, additive property, skewness, kurtosis, recurrence; Poisson as limit of Binomial; normal limit of Poisson.

 UNIT 3

Negative Binomial

Definition, moments, MGF, CF, CGF, PGF, additive property, skewness, kurtosis, recurrence relation, limiting form to Normal.

 UNIT 4

Geometric Distribution

Definition, moments, MGF, CF, CGF, PGF, additive property, skewness, kurtosis, lack-of-memory property, recurrence relation.

 UNIT 5

Hypergeometric Distribution

Definition, mean, variance, problems; recurrence relation; limiting case to Binomial.

 PRACTICAL

Practical Course (9 Experiments)

Fitting Binomial, Poisson, Negative Binomial, Geometric and Hypergeometric distributions by direct & recurrence-relation methods.

 REFERENCE

Official Syllabus

Course outline, textbooks, references and suggested co-curricular activities.
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Next course in learning order: Theoretical Continuous Distributions Probability & distributions