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

Welcome

This is your full, exam-ready study package for Theory of Probability and Mathematical Expectations. Every topic in the syllabus is covered with definitions, axioms, theorems and two worked examples per concept. All formulae are rendered with MathJax for clarity.

Pre-requisite: Set theory, basic counting (permutations & combinations), differential and integral calculus. Probability builds on these.

Course Outcomes

  1. Acquaint with the role of statistics in dealing with univariate random variables.
  2. Learn the extension of univariate data to bivariate data.
  3. Learn to measure randomness mathematically using expectations.
  4. Get familiarity with generating functions, law of large numbers and the Central Limit Theorem.

Units in this Course

UNIT 1

Elementary Probability

Random experiments, sample space, events; classical, statistical and axiomatic definitions; conditional probability, independence; addition, multiplication theorems; Boole's inequality; Bayes' theorem.

 UNIT 2

Univariate Random Variables

Discrete & continuous r.v., functions of r.v., PMF, PDF, distribution function and its properties; moments, skewness, kurtosis from PMF/PDF.

 UNIT 3

Bivariate Random Variables

Joint, marginal and conditional distributions (discrete and continuous); independence of random variables with worked problems.

 UNIT 4

Mathematical Expectation

Expectation, moments & covariance via expectation; addition & multiplication theorems; properties of E, Var, Cov; Chebyshev & Cauchy-Schwarz inequalities.

 UNIT 5

Generating Functions, LLN & CLT

MGF, CGF, characteristic function, PGF and their properties; Weak & Strong Law of Large Numbers; convergence in probability & in distribution; Central Limit Theorem.

 PRACTICAL

Practical Course (7 Experiments)

Moments & coefficients of skewness and kurtosis from PMF and PDF; joint, marginal and conditional distributions; Chebyshev's inequality applications.

 REFERENCE

Official Syllabus

Full course outline, textbooks, references and suggested co-curricular activities.
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Next course in learning order: Probability Theory Probability & distributions