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.
• 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.

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