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

by Hogg, Robert V.  Joeseph McKean  Allen T. Craig
Edition statement:7th ed.
Published by : Dorling Kindersley Pvt. Ltd (New Delhi)
ISBN: 9789332519114
Reference Books

Roussas, George
Published by : Elsevier Academic Press (USA)
Physical details: xii, 387 p. : ill. ; 24 cm.
ISBN: 0120885956 (pbk). 
by Ross, Sheldon
Edition statement:9th ed.
Published by : Pearson Education (New Delhi)
ISBN: 9789332519077 
by Mood, Alexander M.  Franklin A. Graybill  Duane C. BOES
Edition statement:3rd ed.
Published by : McGraw Hill (New Delhi)
ISBN: 0070445206
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Ebooks

by Pleguezuelo, Rafael Herrerías
Publisher: World Scientific
ISBN: 9789812772992 
by Kaur, Berinderjeet
Publisher: World Scientific
ISBN: 9789814313353 
Fienberg, S. Casella, G.
Olkin, I.
Publisher: Springer 
by Dobrow, Robert P
Publisher: John Wiley & Sons 
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Publisher: Walter de Gruyter
ISBN 9783110207484 
by Pleguezuelo, Rafael HerrerÃas
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by Barbour, A. D. Chen, Louis
Chen, Louis H. Y
Publisher: World Scientific
ISBN: 9789812567673