Probability and Probability Distributions I & II: Course Outline Probability and Probability Distributions I
- General Concept of Probability.
- Random Experiment.
- Sample Space and sample points.
- Event; Types of Event.
- Mutually Exclusive.
- Equally likely.
- 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.
- Negative Binomial.
- Beta and Gamma distributions with their properties and application.
- Bivariate Normal distribution.
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