B.Sc. Statistics
2nd Semester Syllabus
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MJC-2 : Theory of Probability (प्रायिकता का सिद्धांत)
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Unit 1: UNIT I
◦Probability: Introduction
◦Random experiments
◦Sample space
◦Events and algebra of events
◦Definitions of Probability
◦Classical
◦Statistical, and axiomatic
◦Laws of addition and multiplication
◦Independence and mutual independence of events
◦Theorem of total probability
◦Conditional probability
◦Baye's theorem and its applications
Unit 2: UNIT II
◦Random variables: discrete and continuous random variables
◦Probability mass function (p.m.f)
◦Probability density functions (p.d.f) and cumulative density function (c.d.f) with illustrations and properties of random variables
◦Univariate transformations with illustrations
◦Two dimensional random variables: discrete and continuous type, joint, marginal, and conditional p.m.f, p.d.f., and c.d.f., independence of variables, bivariate transformations with illustrations
Unit 3: UNIT III
◦Mathematical Expectation and Generating Functions: Expectation of univariate and bivariate random variables and its properties
◦Moments
◦Moment generating function (m.g.f) and characteristic function (c.f.)
◦Uniqueness and inversion theorems (without proof) along with applications
◦Conditional expectation
Unit 4: UNIT IV
◦Standard probability distributions: Binomial
◦Poisson
◦Geometric
◦Negative binomial
◦Hyper-geometric
◦Uniform
◦Normal
◦Exponential
◦Cauchy
◦Beta and gamma along with their properties
Reference Books:
- Hogg, R.V., Tanis, E.A. and Rao J.M. (2009): Probability and Statistical Inference, Pearson Education, New Delhi.
- Miller, Irwin and Miller, Marylees (2006): John E. Freund's Mathematical Statistics with Applications, Pearson Education, Asia.
- Myer, P.L. (1970): Introductory Probability and Statistical Applications, Oxford & IBH Publishing, New Delhi
- Gupta, S. C. and Kapoor, V. K. (2020): Fundamentals of Mathematical Statistics, S. Chand & Sons, New Delhi.