Syllabus for M.Sc Statistics Entrance Exam

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Probability
Conditional Probability
Unconditional Probability
Sample Space - Discrete sample space, Continuous sample space
Event - Operation of Event, Independent Events, Mutually Exclusive Events
Random Experiment
Trial
Baye’s theorem and its application
Random Variables
Approaches to probability - Classical approach to probability, Relative frequency approach to probability, Richard Von Mises approach to probability, Cramer and Kolmogorov’s approach to probability
Moment generating functions
Probability generating functions
Chesbyshev’s inequality and its application

Distributions
Uniform Distribution
Continuous univariate distributions
Normal Distribution
Exponential Distribution
Gamma and Beta Distribution
Binomial Distribution
Poisson distribution
Geometric Distribution
Hyper-geometric Distribution

Types of Data
Graphical representation
Bar diagram
Ogive diagram
Histogram
Frequency Polygon
Measures of central tendency
Dispersion
Qualitative and quantitative Data
Discrete and Continuous data
Primary and Secondary data
Presentation of Data
Construction
Diagrammatic
Relative Dispersion
Absolute Dispersion
Bivariate Data
Scatter diagram
Correlation coefficient
Rank correlation
Spearman’s and Kendall’s measures
Multivariate Data
Multiple correlations in three variables
Partial correlation in three variables
Regression lines
Regression coefficient
Principal of least squares
Analysis of Categorical Data

Sampling
Random sample
Sample tests
Use of central limit theorem for testing and interval estimation
Fisher’s Z transformation
Non- Parametric tests
Wilcoxon- Mann- Whitney test
Run- test
Median- test
Point estimate of a parameter
Concept of bias and standard error of an estimate
Tests of significance based on Chi- square
Testing for the mean and variance of Univarite

Sample Surveys
Concept of population and sampling
Non-Sampling error
Simple random sampling
Stratified random sampling
Systematic sampling
Census and sample survey
Sample selection
Sample size

Linear programming
Transportation Problems
Assignment problems
Elementary theory of convex sets
General linear programming problems (LPP)
Graphical and simplex method of solving LPP

Introduction to computers
Basic set of an electronic computer
Need of computers in statistics
Binary number system
Machine
Language
Basic commands to operate a computer
Ms- Office Tools
CPU
Input devices
Output devices

Demographic Methods
Simple aggregative methods
Weighted average methods
Lasperey’s, Passche’s and Fisher’s index numbers
Sources of demographic data
Measurement of mortality
Measurement of fertility
Economic statistics
Index number

Time series Analysis
Economic time series
Hypothesis
Statistical hypothesis
Simple and composite hypothesis
Statistical hypothesis
Null and alternative hypothesis
Parameter models
Parameter space
Point Estimation
General theory of control charts
Process control chars for variables (X, R and S Charts)
Control chart for attributes (np, p and c charts)
Interval estimation
Concepts of confidence interval and confidence coefficient