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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 Continuous Distributions. Each unit covers one family in depth — definition, PDF, distribution function, moments, MGF/CF/CGF, additive property, skewness, kurtosis and limiting cases — with two worked examples per concept.

Pre-requisite: Courses 1–3. Comfort with calculus (improper integrals, Gamma function), MGFs and discrete distributions is essential.

Course Outcomes

  1. Deal with data using the basic continuous distribution: Uniform.
  2. Acquaint with Exponential distribution and its applications.
  3. Learn Gamma and Beta distributions and their applications.
  4. Familiarize with Normal and Standard Normal distributions in research and applied fields.
  5. Acquire knowledge of exact sampling distributions: \(t\), \(F\), \(\chi^2\).

Units in this Course

UNIT 1

Continuous Uniform Distribution

Definition, moments, MGF, CF, CGF, skewness, kurtosis, distribution function and mean deviation about mean.

 UNIT 2

Exponential Distribution

Definition, moments, MGF, CF, CGF, skewness, kurtosis, distribution function and memoryless property.

 UNIT 3

Gamma & Beta Distributions

Gamma — moments, MGF, CF, CGF, additive property, limiting form. Beta of first and second kind — mean, variance, harmonic mean.

 UNIT 4

Normal Distribution

Definition, importance, MGF, additive property, skewness, kurtosis, mean = median = mode, points of inflexion, linear combination of normal variates.

 UNIT 5

Standard Normal & Sampling Distributions

Standard Normal — area property; population, sample, parameter, statistic, sampling distribution; Student's \(t\), \(F\), \(\chi^2\) — definitions, properties & applications.

 PRACTICAL

Practical Course (7 Experiments)

Moments & shape of Uniform; fitting Exponential and Normal (areas & ordinates); Gamma applications; Standard Normal problems.

 REFERENCE

Official Syllabus

Course outline, textbooks, references and quick reference table for all distributions.
← Back to Course Hub Start with Unit 1 →

Next course in learning order: Distribution Theory Probability & distributions