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Saturday, January 1, 2011

M.Sc.Statistics


M.Sc. Statistics

Note: The syllabus prescribed for the entrance test has been divided into fifteen units. Each unit carries a weightage of four marks. Paper setters are required to set four multiple choice type questions with only one correct or most appropriate answer separately for each unit, giving uniform representation to the whole syllabus contained therein.

Unit-I:
Important concepts in probability: Definition of probability – classical, relative frequency approach to probability, Richard Von Mises, Cramer and Kolmogorov’s approaches to probability, merits and demerits of these approaches (only general ideas to be given).Random Experiment: Trial, sample space, definition of an event, operation of event, mutually exclusive events. Discrete sample space, properties of probability based on axiomatic approach.
Conditional probability, independence of events, Baye’s theorem and its application. Random Variables: Definition of discrete random variables, probability masses function, idea of continuous random variable, probability density function, illustrations of random variables and its properties.

UNIT II:
Moment generating functions (mgf) probability generating function (if it exists), their properties and uses. Standard univariate discrete distributions, their applications and properties (mean, variance, mgf and recurrence relations): Uniform, Binomial, Poisson, Geometric, and Hypergeometric distribution.

UNIT III:
Continuous univariate distributions, their applications and properties (mean, variance, mgf and recurrence relations): Uniform, Normal, Exponential, Gamma and Beta Distributions (first-kind). Chesbyshev’s inequality and its application, weak law of large numbers.

UNIT IV:
Types of Data: Concept of a Statistical population and sample from a population; qualitative and quantitative Data, Discrete and continuous data, primary and secondary data, Presentation of Data: Construction, diagrammatic and graphical representation (Bar diagram, Ogive, Histogram, Frequency Polygon).
Measures of central tendency or location, dispersion and relative and absolute dispersion, Skewness and Kurtosis and their measures including those based on quantiles and moments. Shephard’s corrections for moments for Grouped Data (without derivation).

UNIT V:
Bivariate Data: Scatter diagram; product moment, correlation coefficient and its properties. Limits of the correlation coefficient, effect of change of scale and origin. Rank correlation: Spearman’s and Kendall’s measures.
Multivariate Data: Multiple correlation and partial correlation in three variables.Regression lines and regression coefficient and their properties. Principal of least square and fitting of first-degree polynomial. Analysis of Categorical Data: 2
Consistency of categorical data. Independence and association of attributes. Various measure of association of data.

UNIT VI:
Sampling from a distribution: Definition of a random sample. Concept of statistic and its sampling distribution, point estimate of a parameter, concept of bias and standard error of an estimate. Standard errors of sample mean, sample proportion.
Tests of significance based on Chi- square, testing for the mean and variance of Univarite. Normal distribution. Test for goodness of fit. Contingency table and tests of independence of attributes in a contingency.Definition of t and F statistics. Test for single mean, two means (including paired t-test) and testing of equality of two variances of two-univariate normal distribution. Related confidence intervals for mean and variance of normal distribution.

UNIT VII:
Testing for the significance of sample correlation in sampling from normal population. Large sample tests: Use of central limit theorem for testing and interval estimation of a single mean and a single proportion and difference of two means and two proportions, Fisher’s Z transformation and its uses.
Non- Parametric tests: Its advantages and disadvantages, Sign test for univariate distribution, Wilcoxon- Mann- Whitney test, Run- test, Median- test.

UNIT VIII:
Sample Surveys; Concept of population and sample, need for sampling, Census and sample survey, basis concept in sampling, organizational aspects of survey sampling, sample selection and sample size, Non-Sampling error. Some basic sampling methods:
Simple random sampling (SRS) with and without replacement. Estimation of mean, Its Variance and estimate of its variance.
Stratified random sampling: Estimation of mean, its variance. Advantage of stratified sampling over simple random sampling. Systematic sampling: estimation of mean and its variance.

UNIT IX:
Analysis of Variance, assumptions and applications, ANOVA for one way and two way (using Principle of LSE). ANOVA table its interpretation and related examples. Principles of Design: Local control, Replications, Randomisation.
Basic designs: CRD, RBD LSD and their analysis. Advantages and disadvantages of RBD over CRD.

UNIT X:
Single missing observation analysis for RBD. Latin Square Design (LSD) layout and its analysis. Factorial designs:22,23 designs, illustration, main effects and interaction effects and ANOVA.Yates Method . 3

UNIT XI:
Linear programming: Elementary theory of convex sets, definition of general linear programming problems (LPP), example of LPP, graphical and simplex method of solving LPP, (without artificial variable technique). Concepts of transportation (initial basic feasible) and assignment problems. Introduction to computers Basic set of an electronic computer (CPU, input & output devices) Need of computers in statistics, Binary number system. Machine Language or high-level language. Basic commands to operate a computer. Ms- Excel for discriptive Statistics.

UNIT XII:
Demographic Methods: sources of demographic data- Census Register, and Adhoc Survey. Measurement of mortality, crude, specific and Standard Death Rates, infant mortality rate. Measurement of fertility Crude Birth Rate, General Fertility Rate, Total Fertility Rate.
Economic statistics: Index number: its definition application, of index number. Price relatives and quantity or volume relatives, link and chain relatives, Problems involved in computation of index number, use of averages, simple aggregative and Weighted average methods, Lasperey’s, Passche’s and Fisher’s index numbers, time and factor reversal tests of index number.

UNIT XIII:
Time series Analysis: Economic time series, its different components and additive model. Multiplicative models of time series determination of trend, growth curves, analysis of seasonal fluctuations.
Importance of Statistics methods in industrial research and practice, specification items and lot qualities corresponding to visual gauging, count and measurement. General theory of control charts, process control chars for variables ( X, R and S Charts).Control chart for attributes (np, p and c charts). Production control, consumer’s risk and producers plan, their OC functions, concept of AQL, LTPD, AOQL & ASN function.

UNIT XIV:
Introduction: Parameter models, parameters, Random sample and its likelihood statistics and its sampling distribution. Parameter space. Point Estimation, estimates and estimator. Requirements of a good estimator. Unbiasdness, consistency, efficiency and sufficiency. Maximum likelihood estimation, methods of moment, Minimum Chi square method, least square and minimum variances. (Examples based on these methods).

UNIT XV:
Interval estimation: concepts of confidence interval and confidence coefficient. Confidence intervals for the parameters of univariate normal, two independent normal and one-parameter exponential distribution. Statistical hypothesis, simple and composite hypothesis, test of statistical hypothesis, null and alternative hypothesis. Critical region, two kinds of errors, level of significance and power of a test.