ANDHRA
LOYOLA COLLEGE: VIJAYAWADA
DEPARTMENT
OF STATISTICS
BATCH 201518
SEMESTER

PAPER NO

MAJOR/
ELECTIVE

TITLE

SUBJECT CODE

CREDITS

I

1

Major

Descriptive
Statistics and theory of Probability

STA111

3

II

2

Major

Probability
Distributions

STA122

3

III

3

Major

Statistical
Methods and Exact Sampling Distributions

STA233

3

IV

4

Major

Statistical
Inference

STA244

3

V

5

DSE

Design
of Experiments and Sample Surveys

STA355

3

V

6

DSE

Operations
Research

STA356A

2

VI

7A

DSE*

Applied
Statistics

STA367

3

VI

7B

DSE

Elements
of Stochastic Process

STA367

3

VI

7C

DSE

Time
Series Analysis

STA367

3

VI

Cluster
I

SEC**

(i)
Statistical Quality
Control
(ii)
Optimization
Techniques
(iii)
Basic Statistical Data
Analysis Using R


2

VI

Cluster
II

SEC

(i)
Demography
(ii)
Actuarial Statistics
(iii)
Data Base
Management
Systems

STA368A

2

VI

Cluster
III

SEC

(i)
Econometrics
(ii)
Computational
Techniques
(iii)
Statistical Computing
using C Programming

STA368B

2

General Elective: Biostatistics


1

Project Work


1

*DSEDiscipline Specific Elective **SECSkill
Enhancement Electives

III
B.A / B.Sc. STATISTICS
SEMESTER V: PAPER V
DESIGN OF EXPERIMENTS AND SAMPLE
SURVEYS
UnitI:
Sampling and
sample surveys, concepts of population and sample, need for sampling, census
and sample survey, basic concepts in sampling, Non sampling errors, advantages
of sampling over complete census, limitations of sampling. Some basic sampling
methods  simple random sampling (SRS) with and without replacement.
UnitII:
Stratified
random sampling  Properties of the estimates, unbiased estimates for mean and
variance, Neymannoptimal and proportional allocations, Systematic sampling –
estimation of mean and variance of the estimated mean, comparison of simple,
stratified and systematic sampling.
UnitIII:
Analysis of
variance for oneway & twoway classifications, Need for design of
experiments, fundamental principles of experimentation – randomization,
replication and local control. Description and analysis of variance of
Completely Randomized Design (CRD), Randomized Block Design (RBD).
UnitIV:
Description
and analysis of Latin Square Design (LSD),
2^{2} and 2^{3} factorial experiments main effects, Yates
method of computing factorial Effect total, interaction effects and its
applications.
UnitV:
Present official statistical system in
India, Methods of collection of official statistics. Role of Ministry of
Statistics & Program Implementation (MoSPI), Central Statistical Office
(CSO), National Sample Survey Office (NSSO), and National Statistical
Commission. Government of India’s Principal publications containing data on the
topics such as population, industry and finance
LIST OF BOOKS
FOR STUDY:
 Applied Statistics S.C.Gupta, V.K.Kapoor Sultan Chand & Co,
New Delhi.
 Sampling Techniques,
Cochran
 Applied Statistics Parimal Mukhopadhyay New Central Book
Agency
LIST OF BOOKS
FOR REFERENCE:
 Fundamentals of Statistics (2000), Vol.2., Goon,A.M. Gupta,
M.K. and Das Gupta, B. World Press, Calcutta.
2. Probability
and Statistics in Engineering  Hines, Montogomery et al John Wiley sons
 Design and Analysis of Experiments (1986), Das, M.N. and Giri,
Springer Verlag Pub.
 Statistical Techniques, Darora Singh.
 Design of experiments Montogomary.
 Indian Official Statistical Systems Saluja M.P Statistical
publishing society, Calcutta
III
B.A / B.Sc. STATISTICS
SEMESTER
– V: PAPER – VI
OPERATIONS RESEARCH
UNITI:
Development
of OR, Nature & meaning of OR, Characteristics of OR, Scope of Operations
Research, Features of OR, Management application of OR Role of OR in decision
making, Development of OR in India. Role of computers in OR.
UNITII:
Sequencing
Problem Introduction, Principal Assumptions, Processing n Jobs through two
machines, processing n jobs through three machines, processing two jobs through
m machines.
UNITIII:
Assignment
Problem – introduction, LP formulation of assignment problem, Hungarian method
to solving assignment problem, unbalanced, maximization, restricted assignment
problem.
UNITIV:
Transportation
Problem  Introduction, Linear programming, Matrix form of transportation
problem, Finding an initial basic feasible solution (IBFS) by North West Corner
Rule, Lowest cost Entry method, Vogel’s approximation method, unbalanced,
maximization, optimal solution by using MODI method.
UNITV:
Definition
of Game, Zerosum game, Saddle point, Value of Game, Payoff matrix.
Fundamental Theorem of 2X2 games, Dominance property and modified dominance
property (simple problems).
LIST
OF BOOKS FOR STUDY:
1.
Operations research – S.D. Sharma
2.
Operations research – Taha. H.A.
LIST
OF BOOKS FOR REFERENCE:
1.
Operations research Wagner
2.
Operations research – Kanthi swaroop
3.
Operations research – V.K. Kapoor
III
B.A / B.Sc. STATTISTICS
SEMESTER – VI: PAPER – VII
APPLIED STATISTICS
UNITI:
Sources
of population data, census, rates and ratios. Fertility and mortality tares,
standardized death rates, components of complete and abridged life table,
reproduction rates. Notion of population projection
UNITII:
Introduction
and applications of time series data,Components of time series trend, Periodic
changes & Irregular components, Analysis of time series data, Measurement
of trend graphic method, method of semi averages, moving averages, curve
fittinglinear , quadratic, Power and exponential curves by principle of least
squares.Limitations
UNITIII
Measurement
of Seasonal Fluctuations method of simple averages, ratio to moving average
method, ratio to trend, Link relatives methods. Use of multiplicative model in
measurement of Seasonal Fluctuations
UNITIV:
Construction
and uses of simple and weighted index numbers, reversal tests of index numbers.
Fisher’s ideal index number, Base shifting and splicing. Construction of cost
of living index number and wholesale price index number
UNITV:
Introduction.
Demand and supply, price elasticities of supply and demand. Methods of
determining demand and supply curves. Leontief’s, Pigous’s methods of
determining demand curve from time series data, limitations of these methods Pigou’s method from time series data. Pareto
law of income distribution curves of concentration
BOOKS FOR STUDY:
1. Applied
Statistics S.C.Gupta, V.K.Kapoor Sultan Chand & Co, New Delhi.
2. Applied
Statistics Parimal Mukhopadhyay New Central Book Agency
3. Applied Statistics Telugu Academy
Hyderabad
BOOKS FOR
REFERENCE:
1. Fundamentals of Statistics
(2000), Vol.2., Goon,A.M. Gupta, M.K. and Das Gupta, B. World Press, Calcutta.
2. Basic
Statistics B.L Agarwal Asia New Age Publications
3. Statistical Methods  SP Gupta, Sultan Chand and Sons
III
B.A / B.Sc. STATISTICS
SEMESTER
VI: PAPER – VIII (Cluster Elective)
Statistical Quality Control
UNIT
I
Quality:
Definition, dimensions of quality, historical perspective of quality control
and
improvements
starting from World War II, historical perspective of Quality Gurus and
Quality
Hall of Fame
UNIT
II
Quality system and standards: Introduction to ISO quality
standards, Quality registration. Statistical Process Control  Seven tools of
SPC, chance and assignable Causes of quality variation. Statistical Control
Charts Construction and Statistical basis of 3Ïƒ Control charts, Rational
Subgrouping.
UNIT
III
Control charts for variables: Xbar & Rchart, Xbar &
schart. Control charts for attributes: npchart, pchart, cchart and uchart.
Comparison between control charts for variables and control charts for
attributes.
UNIT
IV
Product
Control: Producer’s Risk, Consumer’s Risk, Acceptance Sampling Plan, Single and
Double sampling plans by attributes, their OC, ASN ( and ATI ), LTPD and AOQL.
Single sampling plan for inspection by variables (onesided specification,
known and unknown s
cases)
UNIT
V
Quality
Systems: ISO 9000 standards, QS 9000 standards. Concept of sixsigma and the
DefineMeasureAnalyseImproveControl (DMAIC) Approach, Precision and accuracy
in measurement systems.
SUGGESTED
READING:
1.
Montogomery, D. C. (2009): Introduction to Statistical Quality Control, 6th
Edition,
Wiley
India Pvt. Ltd.
2.
Goon A.M., Gupta M.K. and Dasgupta B. (2002): Fundamentals of Statistics, Vol.
I
&
II, 8th Edn. The World Press, Kolkata.
3.
Mukhopadhyay, P (2011):Applied Statistics, 2nd edition revised reprint, Books
and
Allied(P)
Ltd.
4.
Montogomery, D. C. and Runger, G.C. (2008): Applied Statistics and Probability
for
Engineers,
3rd Edition reprint, Wiley India Pvt. Ltd.
6.
Hoyle, David (1995): ISO Quality Systems Handbook, 2nd Edition, Butterworth
Heinemann
Publication.
7.
Logothetis, N. (1992). Managing Total Quality; Prentice Hall of India.
8.
Oakland J.S. (1989). Total Quality Management; ButterworthHeinemann.
9.
Mittag H.J. and Rinne H. (1993) Statistical Methods of Quality Assurance.
10.
Montgomery D.C.(1985); Statistical Process Control; John Wiley.
11.
Montgomery D.C.(1999) Design and Analysis of Experiments; John Wiley
24
III
B.A / B.Sc. STATISTICS
SEMESTER
VI: PAPER – VIII (Cluster Elective)
OPTIMIZATION
TECHNIQUES
UNITI:
Introduction
and Definition of General Linear Programming Problem(LPP) , formulation of LPP,
Matrix form of LPP, Graphical Solution of LPP, Simplex Method – Slack
variables.
UNITII:
Simplex
Method – Artificial variable techniques  Big MMethod, Two Phase Method,
Degeneracy problem, Method to resolve Degeneracy.
UNITIII:
Duality,
primal to dual and dual to primal, General rules of converting any primal to
into its Dual, Statement of fundamental theorem of duality, Dual simplex
method.
UNITIV:
Integer
Programming Problem: Introduction and its applications, Branch and Bound (upto
two branch problems only), Gromarey’s Cutting plane method.
UNITV:
Network
diagram representation, time estimates and critical path in network analysis –
Forward pass computations, Backward pass computations, Determination of
critical path (CPM), Project Evaluation and Review Technique (PERT)expected
time, and variance and expected duration of the project with simple examples.
BOOKS
FOR STUDY:
1.
Operations research – S.D. Sharma
2.
Operations research – Taha. H.A.
BOOKS
FOR REFERENCE:
1.
Operations research Wagner
2.
Operations research – Kanthi swaroop
3.
Operations research – V.K. Kapoor
4.
Operations research – Kanthi swaroop and
other.
5.
Linear Programming 
Hadley G
III
B.A / B.Sc. STATISTICS
SEMESTER VI: PAPER – VIII (Cluster Elective)
Basic Statistical Data Analysis Using R
This
skill based course will review and expand upon core topics in probability and
statistics through the study and practice of basic data analysis and graphical
interpretation using `R’.
Unit
I:
R environment, R studioconsole, environment,
output, basic data types, vectors, strings, factors and data frames, R
functionsNumeric string and date functions, R packages importing the packages
in R.
UNIT
II
Learn
how to load data, plot a graph viz. histograms (equal class intervals and
unequal class intervals), box plot, stemleaf, frequency polygon, pie chart, Ogives
with graphical summaries of data
UNIT
III
Generate
automated reports giving detailed descriptive statistics, correlation and lines
of
regression
UNIT
IV
Random
number generation and sampling procedures. Fitting of polynomials and
exponential curves. Application Problems based on fitting of suitable
distribution, Normal probability plot.
UNIT
V
Simple
analysis and create and manage statistical analysis projects, import data, code
editing, Basics of statistical inference in order to understand hypothesis
testing and compute pvalues and confidence intervals.
SUGGESTED
READING:
1.
Gardener, M (2012) Beginning R: The Statistical Programming Language, Wiley
Publications.
2. Braun W J, Murdoch D J (2007): A First Course in Statistical
Programming with R.
Cambridge
University Press. New York
I B.A / B.Sc STATISTICS
I SEMESTER
(PAPER – I)
DESCRIPTIVE
STATISTICS AND THEORY OF PROBABILITY
UNIT –
I
Measures of Central
Tendency: mathematical and positional. Measures of Dispersion: range, quartile
deviation, mean deviation, standard deviation, coefficient of variation.
Moments, central and noncentral
moments, and their interrelationships, Sheppard’s corrections for moments for
grouped data. Measures of skewness based on quartiles and moments and kurtosis based on moments with real life examples.
UNIT –
II
Principle of least squares, fitting of:
straight line (y= ax+b), quadratic (y=ax^{2}+bx+c), power curve (y=ax^{b})
and exponential curves (y=ab^{x}, y=ae^{bx})
UNIT –
III
Introduction to Probability: Definition of probability, various
approaches of probability – Random Experiment, Trial, sample point, event and
sample space, power set, operations of events, mutually exclusive and
exhaustive events. Discrete and Continuous sample space, properties of
probability based on axiomatic approach, Boole’s inequalities, addition theorem
and multiplication theorem of probability conditional probability, independence
of events, Bayes’ theorem and its applications.
UNIT –
IV
Random Variables: Definition of discrete
random variables, probability mass function, idea of continuous random
variable, probability density function, illustrations of random variables and
its properties, transformation of one dimensional random variable.
UNIT –
V
Expectation of a random variable and its
properties, addition and multiplication theorems – raw moments and central
moments, measures of location, dispersion, skewness and kurtosis, Cauchy
Schwartz inequality, probability generating function (if it exists), Moment
generating function (mgf), Characteristic function (cf) cumulant generating
function (cgf), their properties and uses.
BOOKS FOR STUDY:
1.
Mathematical statistics John E Freund,
Ronald E Walpole PHI publications
2.
Fundamentals of Mathematical Statistics,
VK Kapoor, SC
Gupta, Sultan Chand, New Delhi.
3.
Statistics first year Telugu academy
BOOKS FOR REFERENCE:
1.
Probability and Statistics in
Engineering Hines,Montogomery et al John Wiley sons
2.
Fundamentals of statistics, Goon AM,
Gupta MK, das Gupta B, World Press, Calcutta.
3.
New Mathematical Statistics, Sanjay
Aurora and Bansilal.
4. Statistics:
A Beginner’s Text Vol. I, Bhat BR, Srivenkataramana T and Rao Madhava KS,
New age international (P) Ltd.
5. Introduction
to the theory of Statistics, Mood AM, Graybill FA and Bose DC,
McGraw Hill.
6. Introduction
to Mathematical Statistics Robert V Hogg, Allen T Craig, Pearson Education
I B.A / B.Sc STATISTICS
II SEMESTER
(PAPER – II)
PROBABILITY DISTRIBUTIONS
UNIT – I
Bivariate random variable,
discrete and continuous: joint, marginal and conditional distributions,
distribution function of Bivariate random variable, its properties,
mathematical expectation of Bivariate random variable, covariance.
Chebyshev’s
inequality and its applications, statements and applications of weak law of
large numbers and Demovier Laplacecentral Limit Theorem.
UNIT – II
Univariate discrete distributions:
Discrete Uniform, Bernoulli, Binomial, Poisson and their mgf, pgf, cgf, cf,
first four moments, skewness, kurtosis, additive property (if exists),
recurrence relation of central moments and recurrence relation of probability.
UNIT –
III
Univariate discrete distributions: Hyper geometric,
Negative Binomial distributions and Geometric distribution with memory less
property and their mgf, pgf, cgf, cf, first four moments, skewness, kurtosis,
additive property (if exists), recurrence relation of central moments and
recurrence relation of probability.
UNIT – IV
Continuous univariate distributions:
Uniform, Normal distribution their definitions, properties and its importance
in statistics, normal distribution as limiting case of Binomial and Poisson
distributions. Mean, Median, Mode, mgf, cgf, cf and additive property, (if
exists).
UNIT – V
Continuous univariate
distributions: Cauchy, Exponential (with memory lack property), ChiSquare,
Gamma and Beta distributions their definitions, properties and its importance
in statistics, Mean, Median, Mode, mgf, cgf, cf and additive property, (if
exists)
BOOKS
FOR STUDY:
1.
Mathematical statistics John E Freund,
Ronald E Walpole PHI publications
2.
Fundamentals of Mathematical Statistics,
VK Kapoor, SC Gupta, Sultan Chand, New Delhi.
3.
Statistics first year Telugu academy
BOOKS
FOR REFERENCE:
4.
Probability and Statistics in
Engineering  Hines, Montogomery et al John Wiley sons
5.
Fundamentals of statistics Vol.I, Goon
AM, Gupta MK, das Gupta B, World Press, Calcutta.
4.
Discrete Distributions vol 1,
Norman.L.Johnson and Samuel kotz  John Wiely
5.
Continuous Distributions vol 2,
Norman.L.Johnson and Samuel kotz  John Wiely
6.
Introduction to probability theory,
Walpole
7.
New Mathematical Statistics, Sanjay
Aurora and Bansilal.
8. Statistics:
A Beginner’s Text Vol. I, Bhat BR, Srivenkataramana T and Rao Madhava KS, New
age international (P) Ltd.
II B.A / B.Sc. STATISTICS
SEMESTER –
III (PAPER – III)
STATISTICAL
METHODS & EXACT SAMPLING DISTRIBUTIONS
UNIT – I
Bivariate Data:
Scatter diagram, marginal, graphical representation of marginal as well as
bivariate frequency table, conditional frequencies, conditional empirical
distributions, conditional mean. Product moment correlation coefficient and its
properties. Coefficient of determination. Correlation ratio, Spearman’s Rank
correlation and its properties
UNIT – II
Fitting of
simple linear regression and related results, Concept of error in regression
line Multivariate data: Multiple regression line, multiple correlation and
partial correlation in three variables.
UNIT – III
Analysis of
Categorical Data: Consistency of categorical data. Independence and
associations of attributes. Various measures of association for twoway and
threeway classified data Odds ratio.
UNIT – IV
Concept of Population,
parameter, random sample, Statistic. Definition of a random sample, concept of
sampling distribution, Exact sampling distributions – Statements and properties
of Student’s t, c^{2}, F  distributions and inter
relation.
UNIT – V
Point estimate of a parameter, concept of bias and mean square error
of an estimate, Criteria of a good estimator  consistency, unbiasedness,
efficiency and sufficiency, Statement of CramerRao Inequality, MVB of the
estimator of the parameter of Binomial with a given ‘n’, Poisson, Normal with
known ‘s’. Statement of FisherNeymann Factorization theorem, sufficient
statistics of parameters of Binomial, Poisson, Normal and Exponential cases
(one parameter only), Estimation by the method of moments, Maximum Likelihood
(ML) method and the statements of optimum properties of MLE’s, Confidence
intervals for parameters of Normal population (for large sample).
BOOKS
FOR STUDY:
1. Mathematical statistics John E Freund,
Ronald E Walpole PHI publications
2. Fundamentals of Mathematical Statistics, VK Kapoor, SC
Gupta, Sultan Chand,
3. Statistics second year Telugu academy
BOOKS
FOR REFERENCE:
1.
Mathematical Statistics, Freund JE,
prentice Hall of India.
2.
Probability and Statistics in
Engineering  Hines, Montogomery et al John Wiley sons
3. Fundamentals
of statistics Vol.II, Goon AM, Gupta MK, das Gupta B, World Press, Calcutta.
4. Introduction
to the theory of Statistics, Mood AM, Graybill FA and Bose DC,
McGraw Hill.
5. An
Introduction to Probability Theory and Mathematical Statistics, Rohatgi VK,
John Wiley & Sons
II B.A / B.Sc STATISTICS
IV SEMESTER
(PAPER – IV)
STATISTICAL
INFERENCE
UNITI
Statistical
Test: Null and alternative hypotheses, Critical region, Level of significance,
power of a test, Types of errors, pvalues, NeymannPearson lemma for testing a
simple null hypothesis against a simple alternative hypothesis with simple
examples in case of Binomial, Poisson, Exponential, Normal with known standard
deviation.
UNITII
Testing
for the mean and variance of univariate normal distribution, testing of
equality of two means and testing of equality of two variances of two
univariate normal distributions, related confidence intervals. Testing for the significance of sample
correlation coefficient.
UNITIII
Large sample
tests: Use of central limit theorem for testing an interval estimation of a
single mean, single proportion, difference of two means and two proportions,
test for single standard deviation and difference of two standard deviations,
Fisher’s Z transformation and its uses.
UNITIV
Definition
of order statistics and their distributions (in case of exponential only),
Nonparametric tests, their advantages and disadvantages, Sign test, Wilcoxon
signed rank test for one sample and two paired samples, WilcoxonMannWhitney
‘U’ test, Run test, Median test.
UNITV
Pearson’s
Chisquare test for goodness of fit, testing for homogeneity of populations and
test for independence in contingency table.
Sequential
analysis introduction, Sequential probability ratio test (SPRT)  Operating
Characteristic of sequential sampling plan, Average Sample Number function of
sequential sampling plan
BOOKS FOR STUDY:
1. Probability and Statistical inference
Hogg and Tanis,
Pearson Education
2. Fundamentals of Mathematical Statistics, VK Kapoor, SC Gupta, Sultan
Chand, New Delhi.
3. Statistics second year Telugu academy
BOOKS FOR REFERENCE:
1.
Probability and Statistics in
Engineering  Hines, Montogomery et al John Wiley sons
 Statistical Inference , Rohatghi
 Fundamentals of statistics Vol.II, Goon AM, Gupta MK, Das Gupta
B, World Press, Calcutta.
 Introduction to the theory of Statistics, Mood AM, Graybill FA
and Boss DC,
McGraw Hill.
 An Introduction to Probability Theory and Mathematical
Statistics, Rohatgi VK, John Wiley
& Sons.
 Statistics: A Beginner’s Text Vol.II, Bhat BR, Srivenkataramana
T and Ral Madhava KS, New age international (P) Ltd.
 Non parametric statistics for behavioral sciences, Syndev
Seigal.