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Probability and Probability Distributions I & II: Course Outline Probability and Probability Distributions I

The course covers the transformation techniques which are useful for determining the sampling distribution of statistic.

Course Outline

  • General Concept of Probability.
  • Random Experiment.
  • Sample Space and sample points.
  • Event; Types of Event.
  • Mutually Exclusive.
  • Equally likely.
  • Exhaustive.
  • Compliment.
  • Dependent and Independent.
  • Rules for Counting the Sample Points.
  • Multiplicative rule.
  • Permutation and Combination.
  • Definition of Probability.
  • Axioms of Probability.
  • Probability as a set function.
  • Addition Theorem of Probability (ATP).
  • Conditional Probability.
  • Multiplicative Theorem of Probability (MTP). Bayes’ Theorem (BT).
  • Proofs and application of ATP, MTP and BT.
  • Random Variable (RV).
  • Probability Distribution and Probability Density Function.
  • Mean or Expected value and variance of RV.
  • Distribution function.
  • Joint distribution.
  • Marginal and conditional distributions.
  • Stochastic independence.
  • Conditional expectation.
  • Probability generating function.
  • Moment generating function.
  • Characteristics function and their existence properties.
  • Relation between moments and cumulate.
  • Probability Distributions.
  • Binomial.
  • Poisson.
  • Hypergeometric.
  • Multinomial.
  • Negative Binomial.
  • Geometric.
  • Uniform.
  • Normal.
  • Exponential.
  • Beta and Gamma distributions with their properties and application.
  • Bivariate Normal distribution.

Text Book

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