Theory and Practical Papers in each
Semester
( Department of
Statistics )
BA / B.Sc
Semester 1
Paper I : ( S101 ) Probability
Paper II : ( S102 ) Statistical
Methods
Semester II
Paper I : ( S201 ) Probability
distributions and Numerical Analysis
Paper II : ( S202 ) Practicals
Semester III
Paper I : ( S301 ) Statistical
Inference
Paper II : ( S302 ) Analysis
of Variance and Design of Experiment
Semester IV
Paper I : ( S401 ) Survey
Sampling
Paper II : ( S402 ) Practicals
Semester V
Paper I : ( S501 ) Non
– parametric Methods and Regression Analysis
Paper II : ( S502 ) Quality
Control and Economic Statistics
Paper III : ( S503 ) Practicals
Semester VI
Paper I : ( S601 ) Applied
Statistics
Paper II : ( S602 ) Operations
Research
Paper III : ( S603 ) Practicals
SYLLABUS OF STATISTICS
SEMESTER I ( B.Sc / B.A. )
( S101)
Paper I : Probability
UNIT – 1
Random experiment, trial point and sample point and sample space, events operation of events, concepts of equally likely, mutually exclusive and exhaustive events.
Definition of probability :
Classical, relative frequency and axiomatic approaches. Discrete probability
space, properties of probability under set theoretic approach.
UNIT – II
Random variables - discrete and continuous, probability mass function ( pmf ) and probability density function (pdf), Cumulative distribution function (cdf). Joint distribution of two random variables, marginal and conditional distributions.
UNIT – III
UNIT – IV
Moments, moment generating functions ( m.g.f.) and their properties, continuity theorem for m.g.f. ( without proof ). Chebyshev’s inequality. Weak law of large numbers and Central Limit Theorem for a sequence of independently and identically distributed random variables and their applications.
References :
- Parzen, E.S. : Modern Probability Theory and its Applications.
- Meyer, P. : Indroductry Probability and Statistical Applications.
- Stirzekar David ; (1994 ) : Elementry Probability,
- Mood
A.M., Graybill F.A. and
National P.G. College, Lucknow
SYLLABUS OF STATISTICS
SEMESTER I ( B.Sc / B.A. )
( S102)
Paper II : Statistical Methods
UNIT -1
Concept of statistical population, Attributes and variables ( discreete and Continuous ). Different types of scales – nominal, ordinal, ratio and interval. Primary data – designing a questionnaire and schedule, collection of primary data, checking their consistency. Secondary data. Scrutiny of data for internal consistency and detection of errors of recording. Ideas of cross validation . Presentation of data : classification, tabulation, diagrammatic representation of grouped data. Frequency distributions, cumulative frequency distributions and their graphical representations, histogram, frequency polygon and ogives. Stem and leaf plot. Box Plot.
UNIT – II
Measure of central tendency and dispersion, merits and demerits of these measures. Moments and factorial moments. Shephard’s correction for moments. Skewness and Kurtosis and their Measures. Measures based on quartiles. Bivariate data, Method of least squares for curve fitting.
UNIT – III
Correlation and regression, rank Correlation ( Spearman’s and
UNIT - IV
Attributes – Notion and terminology, contingency table,
class frequencies and ultimate class frequencies ,
consistency. Association of attributes,
References
:
- A.M. Goon, M.K. Gupta & B.Dasgupta : Fundamental of Statistics. Vol. 1. The World Press Private Ltd.
- Yule,
G.U. and
- C.E. Weatherburn : Mathematical Statistics
National
SYLLABUS OF STATISTICS
SEMESTER II ( B.Sc / B.A. )
(S201)
Paper I : Probability
distributions and Numerical Analysis
UNIT- I
Univariate distributons :
Binomial, Poission, Hypergeometric, Geometric and Negative Binomial. Uniform (
discrete & contineous ), Normal, Exponential, Gamma, Beta distributions.
Cauchy,Normal and poisson distributions as limiting case of binomial
distribution and practical applications.
UNIT – II
Distributions of
function of random variables : Distribution of sum, product and quotient
of two Variable. Reproductive property of standard distributions. Chi-square, t
and F distributions ( Central cases only ) and their and their limiting forms.
Bivariate normal distribution and its properties.
UNIT – III
Calculus of
finite differences, operators, seperation of symbols, examples and problems.
Interpolation
formulas with remainder term. Newton’s forward and forward and backward
formulae. Central difference formulae, Newton’s divide difference formulae for
interpolation. Lagrange’s interpolation formulae.
UNIT – IV
Numerical
Integration : Derivation of general quadrature formula for equidistant
ordinates. Derivation of trapezoidal, Simpson’s 1/3rd and 3/8th rules. Weddle’s
rule. Real roots of a numerical equation by method of iteration.
References :
- Parzen, E.S. : Modern
Probability Theory and Its Applications.
- Meyer, P. : Introductory
Probability and Statistical Applications.
- Scarborough : Numerical
Analysis.
- S.S. Sastry : Introductory
Methods of Numerical Analysis ; Prentice Hall of India Pvt. Ltd.
- Freeman : Finite Differences.
- Jain, M.K., Iyengar, SRK and Jain
R.K. : Numerical Methods For Scientific And Engineering
Computations ; NEW AGE International (P) Ltd.
National
SYLLABUS OF STATISTICS
SEMESTER II ( B.Sc / B.A. )
( S202 )
Paper II : List of
Practical Experiments
- Graphical representation of data by
Histogram, Frequency Polygons, Frequency
Curves and Ogives. Stem and leaf Plot, Box Plot.
- Calculation of measures of location.
- Calculation of measures of
dispersion.
- Calculation of moments, measures of
skewness and measures of Kurtosis.
- Fitting of curves by method of least
squares.
- Determination of regression lines and
calculation of correlation coefficient – grouped and ungrouped data.
- Calculation of correlation ratios,
rank and intra – class correlation coefficients.
- Calculation of multiple and partial
correlation coefficients for three variables.
- Construction of Index numbers.
- Calculation of measures of
association in contigency tables.
- Construction of forward difference
tables and divide difference tables.
- Interpolation by Newton’s forward
difference formula for equal intervals and calculation of error.
- Interpolation by Newton’s divide
difference formula for unequal intervals. Calculation of error.
- Interpolation by Lagrange’s formula
for unequal intervals. Calculation of error.
- Approximate integration ( Trapezoidal rule, Simpson’s one-third rule, Simpspon’s three-eighth
rule ), Weddle’s rule.
- Real roots of numerical equation by
method of iteration.
All practical would be done in
MS-Word & MS – Excel.
SYLLABUS OF STATISTICS
SEMESTER III (
B.Sc / B.A. )
( S301 )
Paper I : Statistical Inference
UNIT – I
Point estimation .
Requirements of a good estimator : Unbiasedness , consistency, sufficiency and efficiency.
Method of maximum likelihood and properties of Maximum likelihood estimators ( without proof ). Method of minimum Chi-square
. Method of Least squares and methods of moments for estimation of parameters . Problems and examples.
UNIT – II
Sufficient Statistics, Cramer- Rao inequality and its use in finding MVU estimators. Statistical Hypothesis ( simple and composite ). Testing of hypothesis. Type I and Type II errors, significance level, p-values, power of a test. Definitions of Most Powerful ( MP), Uniformly Most Powerful ( UMP ) and Uniformly Most Powerful Unbiased (UMPU) tests.
UNIT – III
Neyman – Pearson’s lemma and its
applications for finding most powerful tests for simple hypothesis against
simple alternative. Tests based on t, F and 
distributions.
UNIT - IV
Likelihood ratio tests and their reduction to standard tests. Large sample tests, variance – stabilizing transformations. Interval estimation, Pivotal quantity and its use in finding confidence intervals, concept of best confidence intervals.
Reference
:
1. Hogg &Craig : Mathematical Statistics.
2. Mood, Graybill and Boes : Introduction to the theory of Statistics.
3. Goon, Gupta and Dasgupta : Fundamentals of Statistics Vol. I & II
National P.G. College, Lucknow
SYLLABUS OF STATISTICS
SEMESTER III (
B.Sc / B.A. )
( S302 )
Paper II : Analysis of Variance and Design of Experiment
UNIT – I
Analysis of Variance ( with fixed
effects model ). One way classification. Assumptions regarding model. Two way classification with
equal number of observations per cell .
UNIT – II
Principles of Design of experiments : Randomization , Replication and local control. Choice of size and type of a plot using uniformity trials. CRD, Randomized block design. Concept and definition of efficiency of design. Comparison of efficiency between CRD and RBD.
UNIT - III
Latin square Design, Lay-out , ANOVA table. Comparison of efficiencies between LSD and RBD; LSD and CRD. Missing plot technique : estimation of missing plots by minimizing error sum of squares in RBD and LSD with one or two missing observations.
UNIT - IV
Factorial Experiments : general
description of factorial experiments; 2
,2
and 2
factorial experiments arranged in RBD . Definition
of main effects and interactions in 2 and 2 factorial experiments. Preparation
of ANOVA by Yates procedure. Estimates and tests for main and
interaction effects ( Analysis without confounding).
Reference
:
1Cochran and Cox : Experimental Design
1
Kempthorne :
Design of Experiments
2
Federer :
Experimental Design
3
Goon, Gupta and Dasgupta
: Fundamentals of Statistics, Vol. II
National
SYLLABUS OF STATISTICS
SEMESTER IV (
B.Sc / B.A. )
( S401 )
Paper I : Survey Sampling
UNIT – 1
Sampling Vs complete enumeration : sampling units and frame. Precision and efficiency of estimators. Simple Random sampling with and without replacement. Use of random number tables in selection of simple random sample. Estimation of population mean and proportion. Derivation of expression for variance of these estimators. Estimation of variances. Sample size determination.
UNIT - II
Stratified random sampling. Problem of allocation, proportional allocation, optimum allocation. Derivation of the expressions for the standard errors of the usual estimators when these allocations are used. Gain in precision due to stratification. Role of sampling cost in the sample allocation. Minimization of variance for fixed cost. Systematic sampling : estimation of population mean and population total, standard errors of these estimators.
UNIT - III
Regression and ratio methods of estimation in simple random sampling. Cluster sampling with equal and unequal clusters. Estimators of population mean and their mean square error.
UNIT – IV
Double sampling in ratio method of estimation. Two- stage sampling with equal first stage units : estimator of population mean and its variance, Multi - stage sampling with examples ( definition only ). Non- sampling errors.
Reference
:
1 Cochran, W. G.: Sampling Techniques
2 Sukhatme, Sukhatme, Sukhatme & Asok: Sampling Theory of Surveys with applications.
3 Murthy, M.N. : Sampling Theory
National
SYLLABUS OF STATISTICS
SEMESTER IV (
B.Sc / B.A. )
( S402 )
Paper II : List
of Practical Experiments
1 Fitting of Binomial, Poisson and Normal distributions to observed data and testing of goodness of fit.
2
Testing of independence of attributes in m x
n contingency table and calculation of measures of association.
3
t – test for (i )
=
( ii ) 
=
( iii ) 
( iv ) 
( v ) 
(vi ) 
= 0
4
F-test for ( i ) 
= 
( ii ) 
= 0
5
Fisher’s Z – transformation and its use in
testing ( i ) 
= 
( ii )
= 
( iii)
= = …= 
6
Calculation of power curve for testing H : = 
against H
: 
for a normal
distribution with known variance.
7 Large sample tests.
8 Analysis of variance in one-way and two-way classification ( with and without interaction terms ) with fixed effects.
9 Analysis of CRD, RBD and LSD.
10 Analysis of CRD, RBD and LSD with one or two missing observations.
11 Drawing a simple random sample with the help of table of random numbers.
12 Estimation of population means and variance in simple random sampling.
13 Stratified random sampling for population mean [ proportional and optimum (Neyman case ) allocation ] .
14 Ratio and regression methods of estimation of population mean and total.
15
Factorial Experiment ( 2 and 2 only ).
National
SYLLABUS OF STATISTICS
SEMESTER V (
B.Sc / B.A. )
( S501 )
Paper I : Non – parametric
Methods and Regression Analysis
UNIT – 1
Multivariate normal distribution, marginal and conditional distribution, Moment generating and Characteristics functions of multivariate normal distribution, Maximum likelihood estimation of mean vector and co-variance matrix of multivariate normal distribution. . Distribution of linear combination of components of multi normal variate.
UNIT – II
Order Statistics. Distributions of minimum, rth and maximum order statistic. Joint distribution of rth and sth order statistics ( in continuous case ) Distribution of sample range & sample median, for uniform and exponential distributions. Confidence interval of quantiles of order p.
UNIT - III
Non – parametric tests – tests for randomness and test for goodness of fit. One sample tests : sign test, Wilcoxon signed rank tests. Two sample tests : run test, Kolmogorov – Smirnov’s test. Median test and Mann – Whitney U test. Mood tests and Sukhatme test for scale parameter, Spearman’s rank correlation test, Kurskall – Wallis Test.
UNIT – IV
Linear regression model of full rank,
Least squares theory. Estimation of parameters – OLSE
and MLE of 
and test of
hypothesis. R and adjusted R. ANOVA table for regression.
Reference
:
1
Mood, A.M., Graybill
and
1 Gibbons, J.D. : Non – parametric statistical inference.
2 Conover, W.J. : Practical Non-parametric Statistics
3 David, H.A. : Order Statistics
4
5
SYLLABUS OF STATISTICS
SEMESTER
V ( B.Sc / B.A. )
( S 502 )
Paper II : Quality Control
and Economic Statistics
UNIT - I
Time series : Definition,
components of time series ,
additive and multiplicative models, measurement of trend, measurements
of seasonal fluctuations, measurement of cyclical fluctuations, Variate difference method. Idea of Periodogram and correlogram.
UNIT - II
Index number : Definition , price relative and quanitity or volume relatives. Problems in the construction of index number, use of averages , simple aggregative and weighted average method . laspeyre’s , Paasche’s Marshall Edgeworth Fisher’s index number. Tests for index numbers - time and factor reversal tests of index number . Chain index , Cost of living index number, Use of index number and limitations of index numbers.
UNIT - III
Quality of a product , need for quality control, Process and Product control,
General theory of control charts, Causes of variation in quality. Control, specification and tolerance limits. Control chart for the attributes : p- chart, np – chart, c – chart, u – chart. Chart for variables : chart for average, range and standard deviation, modified control charts, group control charts, CUSUM charts.
UNIT - 1V
Sampling inspection by attributes – single and double sampling plans. Producer’s and consumer’s risk, OC, ASN, ATI functions AOQL and LTPD of sampling plans. Sampling inspection by variables - simple cases.
References :
1
2 Burr : Industrial Quality Control
3 Wetherill & Brown ; Statistical Quality Control
4 Siya Ram : Applied Statistics
5 Goon, Gupta and Dasgupta : Fundamental of Statistics ( Vol. II )
SYLLABUS OF STATISTICS
SEMESTER V ( B.Sc / B.A. )
( S503 )
Paper III : Staistics Practical
: Practicals
based on Non Parametric tests,
Time Series, Index Numbers and Quality Control with reference to the syllabus
mentioned in S -- 501 and S – 502.
National
SYLLABUS OF STATISTICS
SEMESTER
VI ( B.Sc / B.A. )
( S601 )
Paper I : Applied Statistics
UNIT - 1
Educational statistics : Scaling procedures – Scaling of test items, test scores, rating of qualitative answers and judgements. Test theory, Linear model of test theory, paraller tests, true score, error variance, tetra – choric, bi- serial and point bi- serial correlation coeeficient.
UNIT - II
Reliability : Definition, methods
of estimating reliability, Test length,
effect of test length on the reliability of a test. Validity of a test : Its definition, various types of Validities and their
measurements.
UNIT - III
Vital Statistics Methods : Methods of obtaining Vital statistics - census, register, ad-hoc survey, hospital records. Measurement of mortality - crude, specific and standardized death rates, infant mortality rates, death rate by cause, age specific death rates, complete life table, its main features and construction. Measurement of fertility – crude birth rate, general fertility rate, age specific fertility rate, total fertility rate, gross reproduction rate and net reproduction rate.
UNIT - IV
Demand Analysis – Demand and Supply , Law of Demand and Supply, Price elasticity of demand, Price elasticity of Supply, Partial elasticities of demand, types of data required for estimating elasticities, Pigous’s method. Engel’s curve and Engel’s law. Income elasticity of demand.
Reference :
1 Croston F.E. and Cowden D.J. : Applied General Statistics
2 Goon, Gupta and Dasgupta : Fundamentals of Statistics, ( Vol. I & II )
3 Siya Ram : Applied Statistics
4 Garrett H.E. : Statistics in Psychology and Education
5
6 Spiegelman M : Introduction to Demography
National
SYLLABUS OF STATISTICS
SEMESTER VI ( B.Sc / B.A. )
( S602 )
Paper II :
Operations Research
UNIT – I
General linear programming problems and their formulations. Methods for solving LPP : Graphical Method, Simplex method , Big- M method, Two phase Method Duality in LPP.
UNIT – II
Transportation problem: North – west corner rule, Least cost method, Vogel’s approximation method. Optimum solution : Stepping stone method, Method of Multipliers. Assignment Problem :Hungarian Algorithm.
.
UNIT – III
Queueing Methods – M/M/1, M/M/C models waiting time distribution for M/M/1, Little’s formulae.
Project Management: PERT/CPM determination of floats construction of time chart and resources labeling.
UNIT – IV
Theory of Games – Two- Person Zero – Sum Games, Pure Strategies ( Minimax and Maximin Principles ) : Games With Saddle Point, Mixed Strategies : Game Without Saddle Point, Principles of Dominance, Solution Methods of Games Without Saddle Point – Algebraic method, Arithemetic method, Marix method, Graphical method, Linear Programming method.
Job sequencing : n jobs – machines, n jobs – K machines, 2 jobs – n machines.
Reference:
1 Swarup Kanti, Gupta P.K. and Man Mohan : Operations Research, Sultan Chand & Sons.
2
Taha, H.A. : Operations Research, Mac Millan
publishing.
National
SYLLABUS OF STATISTICS
SEMESTER VI (
B.Sc / B.A. )
( S 603 )
Paper III : Statistics Practical : Practicals based on Educational
Statistics, Vital Statistics, Demand Analysis and Operations Research
with reference to syllabus mentioned in S – 601 and S - 602.