**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.