B.A/B.Sc., STATISTICS (WITH MATHMATICS)
REVISED SYLLABUS
CBCS/SEMESTER SYSTEM (W.E.F 2020-21 ADMITTED BATCH)
SEMESTER – II
PAPER – II: PROBABILITY THEORY AND DISTRIBUTIONS
UNIT-I
Introduction to Probability: Basic Concepts of Probability, random experiments, trial, outcome, sample space, event, mutually exclusive and exhaustive events, equally likely and favourable outcomes. Mathematical, Statistical, axiomatic definitions of probability. Conditional Probability and independence of events, Addition and multiplication theorems of probability for 2 and for n events. Boole’s inequality and Baye’s theorem
UNIT-II
Random variable: Definition of random variable, discrete and continuous random variables, functions of random variable. Probability mass function. Probability density function, Distribution function and its properties. For a given pmf, pdf calculation of Mean and Variance. Bivariate random variable – meaning, joint, marginal and conditional Distributions, independence of random variables
UNIT- III
Mathematical expectation : Mathematical expectation of a random variable and function of a random variable. Moments and covariance using mathematical expectation with examples. Addition and Multiplication theorems on expectation. Definitions of M.G.F, C.G.F, P.G.F, C.F and their properties (Derivations not required). Chebyshev and Cauchy – Schwartz inequalities.
UNIT-IV
Discrete Distributions: Binomial, Poisson, Negative Binomial, Geometric distributions: Definitions, means, variances, M.G.F, C.F, additive property if exists. Possion approximation to Binomial distribution. Hyper-geometric distribution: Definition, mean.
UNIT – V
Continuous Distributions: Rectangular, Exponential, Gamma, Beta Distributions: mean,variance, M.G.F, C.F. Normal Distribution: Definition, Importance, Properties, M.G.F, CF, additive property.
Text Books:
- K.Kapoor and S.C.Gupta: Fundamentals of Mathematical Statistics, Sultan Chand & Sons, New Delhi.
- BA/BSc I year statistics – descriptive statistics, probability distribution – Telugu Academy- Dr M.JaganmohanRao,DrN.Srinivasa Rao, Dr P.Tirupathi Rao, Smt.D.Vijayalakshmi.
- V.S. Sarma: Statistics Made Simple: Do it yourself on PC. PHI
Reference books:
- Willam Feller: Introduction to Probability theory and its applications. Volume – I, Wiley
- Goon AM, Gupta MK, Das Gupta B : Fundamentals of Statistics , Vol-I, the World Press Pvt.Ltd.,
- Hoel P.G: Introduction to mathematical statistics, Asia Publishing
- JaganMohan Rao and Papa Rao: A Text book of Statistics Paper-I.
- Sanjay Arora and Bansi Lal: New Mathematical Statistics: Satya Prakashan , New Delhi 6.Hogg Tanis Rao: Probability and Statistical Inference. 7th edition. Pearson.