B.Sc. Statistics

The Mahatma Gandhi Kashi Vidyapeeth offers B.Sc. Statistics course to its students. The course structure for it is as follows:

Statistical Methods
Unit-I
General nature and scope of Statistical methods, collection, compilation and tabulation of Statistical data, diagrammatical representation, frequency distribution and principles governing their formulation, representation by graphs.
Unit-II
Measure of Location and dispersion, moments, Sheppard’s (without proof) for moments up to fourth order, measure of skewness and kurtosis.
Unit-III
Bivariate data, scatter diagram, correlation and regression, correlation ratio, intraclass correlation, rank correlation, partial and multiple correlation coefficient in the case of three variables, curves fitting by least square principle.
Unit-IV
Theory of attributes, consistency of data, independence of attributes, association and measures thereof.

Probability & Statistical Inference

Mathematical and Statistical definition of Probability, Axiomatic approach to probability for the discrete case only, Theorems of Total and compound probability, conditional probability, Baye’s theorem, independence of events in probability for two and three events.

Discrete and continuous random variable, probability functions and probability density functions, Distribution Function, Two dimensional random variables, marginal and conditional distribution.

Mathematical expectation, theorems for the expectation of the sum and products of the independent random variables, conditional expectation. Moment generating function and its properties.
Study of some standard distribution-Binomial, Poisson, Hypergeometric, Negative Binomial, Rectangular, Normal, Beta and Gamma Distributions.

Theory of point estimation, Criteria of a good estimator: unbiasedness, consistency, efficiency and Sufficiency (definition), Maximum likelihood estimators and statement of its properties.
Elements of testing of hypothesis, simple and composite hypothesis, two kinds of errors, power, size, test of significance, Level of Significance.

Definition of 2 , t and F distributions and their main characteristics (without proof). Test based on Normal, 2 , t and F distributions and Z-transformation and its applications. Official, Economics, Vital Statistics & Statistical Quality Control Sampling Theory and Design of Experiment Statistical Inference Sampling Distributions Numerical Methods