KAKARAPARTI BHAVANARAYANA COLLEGE (AUTONOMOUS)(Sponsored by S.K.P.V.V.Hindu High Schools’ Committee)

Kothapeta, Vijayawada(An Autonomous College in the Jurisdiction of Krishna University)

ISO-9001-2008 CERTIFIED INSTITUTION NAAC ‘A’ GRADEDESCRIPTIVE STATISTICS AND PROBABILITY THEORY

SEMESTER – I SYLLABUS

Objectives

The aim of this course is to provide basic knowledge in data collection, central tendency, probabilityand random variables

Learning outcomes

1. Understand the nature of the data viz., uniformity in hetrogenity and hetrogrnity inuniformity

2. Determine the probabilities of occurrences and non occurrences of univariate and bivariatedata

U nit-I

Introduction to Statistics: Concepts of Primary and Secondary data. Methodsof collection and editing of primary data, Secondary data.Designing aquestionnaire and a schedule. Measures of Central Tendency - Mean, Median,Mode,Geometric Mean and Harmonic Mean.

U nit-I I

Measures of dispersion: Range, Quartile Deviation, Mean Deviation andStandard Deviation. Descriptive Statistics -Central and Non-Central momentsand their interrelationship. Sheppard's correction for moments.Skewness andkurtosis.

U nit-I I I

Introduction to Probability: Basic Concepts of Probability, randomexperiments, trial, outcome, sample space, event, mutually exclusive andexhaustive events, equally likely and favourable outcomes. Mathematical,Statistical, axiomatic definitions of probability. Conditional Probability andindependence of events,

U nit-I V

Probability theorems:Addition and multiplication theorems of probability for 2and for n events. Boole's inequality and Baye's theorems and problems basedon Baye's theorem.

U nit-V

Random variable: Definition of random variable, discrete and continuousrandom variables, functions of random variable. Probability massfunction.Probability density function, Distribution function and itsproperties.Bivariate random variable - meaning, joint, marginal and conditionalDistributions, independence of random variables.

Practicals - Semester – I

Conduct any 6 (Ms-exel is compulsory)

1. Computation of mean, median and mode.

2. Computation of quartile deviation.

3. Computation of mean deviation

4. Computation of Standard deviation.

5. Non-central moments and central moments, Sheppard corrections&Skewness based on moments and Kurtosis

6. MS-Excel methods for the above Serial numbers 1,2,3,4.

Note: MS-Excel methods to be made mandatory for all the Semesters afterproper training only to the teaching staff by the University concerned.

9 Text Books:

1. V.K.Kapoor and S.C.Gupta: Fundamentals of Mathematical Statistics,Sultan Chand & Sons, New Delhi.

2. 2 BA/BSc I year statistics - descriptive statistics, probability distribution -Telugu Academy - Dr M.JaganmohanRao,DrN.SrinivasaRao, DrP.TirupathiRao, Smt.D.Vijayalakshmi.

3. 3. K.V.S. Sarma: Statistics Made Simple: Do it yourself on PC. PHI

Reference books:

1. Willam Feller: Introduction to Probability theory and its applications.Volume –I, Wiley

2. Goon AM, Gupta MK, Das Gupta B : Fundamentals of Statistics , Vol-I, theWorld Press Pvt.Ltd., Kolakota.

3. Hoel P.G: Introduction to mathematical statistics, Asia Publishing house.

4. M. JaganMohanRao and Papa Rao: A Text book of Statistics Paper-I.

5. Sanjay Arora and BansiLal: New Mathematical Statistics: SatyaPrakashan, New Delhi

6. Hogg Tanis Rao: Probability and Statistical Inference. 7th edition.Pearson.

KAKARAPARTI BHAVANARAYANA COLLEGE (AUTONOMOUS)(Sponsored by S.K.P.V.V.Hindu High Schools’ Committee)

Kothapeta, Vijayawada(An Autonomous College in the Jurisdiction of Krishna University)

ISO-9001-2008 CERTIFIED INSTITUTION NAAC ‘A’ GRADEDESCRIPTIVE STATISTICS AND PROBABILITY THEORY

Answer any five of the following 5x5=25M

1. Explain questionnaire2. Uses of GM and HM3. Explain coefficient of variation4. Explain sheppard’s correction5. Define i) mathematical probability and ii) statistical probability6. Define pair wise independent events7. Define marginal functions8. State baye’s theorem

Answer the following questions 5X10=50M

9. a) Explain primary and secondary data and also the sources of primary dataOr

b) calculate mean and median of the following data

C.I 0 - 5 5-10 10-15 15-20 20-25 25-30 30-35 35-40F 8 14 17 22 23 19 18 11

10. Derive the relationship between central and non central momentsOr

Explain skewness and kurtosis

11. Define the following i) Mutually exclusive Events ii) exhaustive events iii) axiomatic definitionof probability

Or

When three coins are tossed find the probability of getting i) at least 2 heads ii) atmost 1head iii) two tails or one head

12. State and prove Addition theorem of probability for ‘n’ events

Or

State and prove BOOLE’s inequality

13. Define distribution function and state its propertiesOr

b) A random variable X has the following probability function

X -2 -1 0 1 2 3P(x) k 3k 5k 8k 12k 6k

i) Find Kii) Mean and varianceiii) Cumulative distribution

KAKARAPARTI BHAVANARAYANA COLLEGE (AUTONOMOUS)(Sponsored by S.K.P.V.V.Hindu High Schools’ Committee)

Kothapeta, Vijayawada(An Autonomous College in the Jurisdiction of Krishna University)

ISO-9001-2008 CERTIFIED INSTITUTION NAAC ‘A’ GRADEMATHEMATICALEXPECTATION AND PROBABILITY DISTRIBUTION

SEMESTER – II SYLLABUS

Objective

The aim of this course is to provide knowledge about various patterns of variousdistributions both discrete and continuous.

Learning outcomes

1. Identify the probability functions and patterns of various discrete and continuousdistributions

2. Understand the normal distribution the parent distribution, the area property whichserves as base of sampling theory

Unit-I

Mathematical expectation : Mathematical expectation( ME) of a random variable andfunction of a random variable. Moments and covariance using mathematical expectationwith examples.Addition and Multiplication theorems on expectation.Definitions of M.G.F,C.G.F, P.G.F, C.F its properties.Chebyshev and cauchy - Schwartz inequalities.

U nit-I I

Discrete Distributions : Binomial and Poisson distributions, their definitions, 1st to 4 centralmoments, M.G.F, C.F, C.G.F, P.G.F, mean, variance, additive property if exists. Possionapproximation to Binomial distribution.

U nit-I I I

Negative Binomial, geometric, hyper geometric distributions - Definitions, means,variances, M.G.F, C.F, C.G.F, P.G.F, reproductive property if exists. Binomial approximationto Hyper Geometric Distribution, Poisson approximation to Negative binomial distribution.

U nit-I V

Continuous Distributions : Rectangular, Exponential, Gamma, Beta Distributions of twokinds. Other properties such as mean ,variance,M.G.F, C.G.F, C.F, reproductive property.

Unit - V

Normal Distribution: Definition, Importance, Properties, M.G.F, additive properties,Interrelation between Normal and Binomial, Normal &Poisson distribution. CauchyDistribution .

Text Books:

1. V.K.Kapoor and S.C.Gupta: Fundamentals of Mathematical Statistics, Sultan Chand &Sons, New Delhi.

2. BA/BSc I year statistics - descriptive statistics, probability distribution - Telugu Academy -Dr M.JaganmohanRao,DrN.SrinivasaRao, Dr P.TirupathiRao, Smt.D.Vijayalakshmi

3. K.V.S. Sarma: Statistics Made Simple: Do it yourself on PC. PHI.

Reference books:

1. WillamFeller : Introduction to Probability theory and its applications. Volume –I, Wiley

2. Goon AM, Gupta MK, Das Gupta B : Fundamentals of Statistics , Vol-I, the World PressPvt.Ltd., Kolakota.

3. Hoel P.G: Introduction to mathematical statistics, Asia Publishing house.

4. M. JaganMohanRao and Papa Rao: A Text book of Statistics Paper-I.

5. Sanjay Arora and BansiLal: New Mathematical Statistics: SatyaPrakashan , New Delhi

6. Hogg Tanis Rao: Probability and Statistical Inference. 7th edition Pearson.

Practicals - Semester – II

Conduct any 6 (Ms-exel is compulsory)

1. Fitting of Binomial Distribution – Recurrence relation method.

2. Fitting of Poisson Distribution - Recurrence relation method.

3. Fitting of Negative Binomial Distribution.

4. Fitting of Geometric Distribution.

5. Fitting of Normal Distribution - Areas methods.

6. Fitting of Normal Distribution - Ordinates methods.

7. MS-Excel methods for the above Serial Numbers 1 and 2

KAKARAPARTI BHAVANARAYANA COLLEGE (AUTONOMOUS)(Sponsored by S.K.P.V.V.Hindu High Schools’ Committee)

Kothapeta, Vijayawada(An Autonomous College in the Jurisdiction of Krishna University)

ISO-9001-2008 CERTIFIED INSTITUTION NAAC ‘A’ GRADEMATHEMATICAL EXPECTATION AND PROBABILITY DISTRIBUTION

SEMESTER-II

MODEL PAPERSECTION-A

Answer any five of the following 5x5=25

1.Find the expected number of heads when 3 coins are tossed2.Let X be a random variable with probability distribution

X : 0 1 2 3P(x): 1/3 1/2 1/24 1/8Find mean and variance

3. State and prove addition theorem of expectation4. The mean and variance of binomial distribution are 16 and 8 respectively

find parameters n,p5. If the mean of poisson distribution is 3 find i) p(0<X<3) ii) p(X>0)6. Find the mean of hyper geometric distribution7. Find the m.g.f of rectangular distribution8. Give the properties of normal distribution

SECTION-B

Answer all the for following 5x10=50

9. a) Explain m.g.f and its properties(or)

b) state and prove Cauchy – scwartz inequality

10.a) Derive the mean and variance of binomial distribution(or)

b) Show that poisson distribution is a limiting distribution of binomialdistribution

11.a) Derive m.g.f of geometric distribution and hence mean and variance(or)

b) Explain negative binomial distribution12.a) Derive c.g.f of gamma distribution and hence find mean and variance

(or)b) Derive mean and variance of beta distribution of I kind

13.a) Define normal distribution and hence find m.g.f(or)

b)Explain Cauchy distribution

KAKARAPARTI BHAVANARAYANA COLLEGE (AUTONOMOUS)(Sponsored by S.K.P.V.V.Hindu High Schools’ Committee)

Kothapeta, Vijayawada(An Autonomous College in the Jurisdiction of Krishna University)

ISO-9001-2008 CERTIFIED INSTITUTION NAAC ‘A’ GRADESTATISTICAL METHODS

SEMESTER – III SYLLABUS

Objectives

The aim of this course is to provide knowledge about bivariate data, the relation between them andassociation of attributes

Learning objectives1. Understand the least square concept and predict the future values2. The relation and association between the variables3. Predict the future values based on regression analysisUnit-I

Correlation: Def.,scatter diagram ,its coefficient and its properties. , scatter diagram,computation of correlation coefficient for ungrouped data. spearman's rank correlationcoefficient, properties of spearrman's correlation coefficients and problems.

Unit-II

Regression: simple linear regression, properties of regression coefficients. Regression lines,Concept of Correlation ratio, partial and multiple correlation coefficients, correlation versesregression and their problems.

Unit – III

Curve fitting: Method of least square - Fitting of linear, quadratic, Exponential and powercurves and their problems.

Unit-IV

Attributes : Introduction, Nature, and consistency and mention its conditions. Independenceand association of attributes, co-efficient of association, coefficients of contingency andtheir problems.

Unit –V

Exact sampling distributions: Concept of population, Parameter, random sample, statistic,sampling distribution, standard error. Statement and Properties of χ2, t, F distributions andtheir inter relationships.

Text books

1. BA/BSc II year statistics - statistical methods and inference - Telugu Academy by A.Mohanrao, N.Srinivasa Rao, Dr R.Sudhakar Reddy, Dr T.C. Ravichandra Kum.

2. K.V.S. Sarma: Statistics Made Simple: Do it yourself on PC. PHI.

3. Fundamentals of Mathematics statistics: VK Kapoor and SC Guptha.

Reference Books:

1. Outlines of statistics, Vol II : Goon Guptha, M.K.Guptha, Das Guptha B.

2. Introduction to Mathematical Statistics : Hoel P.G. Practicals - Semester –III Conduct any 6(Ms-exel is compulsory) 1. Fitting of straight line. 2. Fitting of exponential curves.

3. Fitting of power curve.

4. Computation of correlation coefficient & Fitting of Regression lines.

5. Rank correlation coefficient.

6. Computation of Contingency coefficients.

7. MS-Excel methods any for the Serial Numbers 1,2,4,5

KAKARAPARTI BHAVANARAYANA COLLEGE (AUTONOMOUS)(Sponsored by S.K.P.V.V.Hindu High Schools’ Committee)

Kothapeta, Vijayawada(An Autonomous College in the Jurisdiction of Krishna University)

ISO-9001-2008 CERTIFIED INSTITUTION NAAC ‘A’ GRADESTATISTICAL METHODS

SEMESTER-III

MODEL PAPERSECTION-A

Answer any five of the following 5x5=25

1. Explain scatter diagram and it’s properties.2. Define rank correlation and explain formula in the case of tied ranks.3. Explain the angle between two regression lines.4. Explain partial correlation.5. Explain the principle of least squares with examples.6. Explain consistency of attributes.7. Explain coefficient of colligation.8. Explain standard error and sampling distribution.

SECTION-B

Answer all for the following 5x10=50

9. a) Define correlation coefficient and find limits of spearman’s correlationcoefficient.

(or)b)Derive the formula for rank correlation coefficient

10. a) Derive the regression lines for y on x.(or)

b) Explain the properties of regression lines.

11. a) Derive the normal equations for second degree parabola

(or)

b) Derive the normal equations for exponential equations

12. a) Explain criteria for consistency of attributes

(or)

b) Derive the relationship between Q and Y

13. a) Define X^2 distribution and it’s properties

(or)

b) Derive the relationship between t and F

KAKARAPARTI BHAVANARAYANA COLLEGE (AUTONOMOUS)(Sponsored by S.K.P.V.V.Hindu High Schools’ Committee)

Kothapeta, Vijayawada(An Autonomous College in the Jurisdiction of Krishna University)

ISO-9001-2008 CERTIFIED INSTITUTION NAAC ‘A’ GRADESTATISTICS INFERENCE

SEMESTER – IV SYLLABUS

Obvjectives

The aim of this course is provide knowledge about estimation of parameters, testing ofhypothesis concept for large small samples.

Learning outcomes1. Understand the concept of estimation and estimating the parameters based onsample statistic2. Understand the concept of testing of hypothesis, setting of null and alternativehypothesis, tests for small and large samplesUNIT I

Theory of estimation: Estimation of a parameter, criteria of a good estimator –unbiasedness, consistency, efficiency, &sufficiency and. Statement of Neyman'sfactorization theorem. Estimation of parameters by the methods of moments and maximumlikelihood (M.L), properties of MLE’s. Binomial, Poisson &Normal Population parametersestimate by ML method. Confidence intervals of the parameters of normal population.

UNIT II

Concepts of Statistical hypothesis: Null and alternative hypothesis, critical region, two typesof errors, level of significance, power of a test. 1 tailed, 2 tailed tests, Neyman - Pearson'slemma. Examples in of Binomial. Poisson, Normal distributions.

Unit-III

Large Sample Tests : Large sample tests for single mean, two means, Single proportion, Twoproportions, Standard Deviation of single and double samples and Fisher’s Z transformation.

Unit-IV

Small sample tests: Tests of significance based on χ2, t and F. χ2-test for test forindependence of attributes, t-test for single, double and paired tests, Variance Ratio Test(F-test).

Unit-V

Non-parametric tests - Advantages and Disadvantages. Two sample run test, Two sampleMedian test and Two sample sign test.

TEXT BOOKS

1. BA/BSc II year statistics - statistical methods and inference - Telugu Academy byA.Mohanrao, N.Srinivasa Rao, Dr R.Sudhakar Reddy, Dr T.C. Ravichandra Kumar.

2. K.V.S. Sarma: Statistics Made Simple: Do it yourself on PC. PHI.

REFERENCE BOOKS:

1. Fundamentals of Mathematics statistics : VK Kapoor and SC Guptha.

2. Outlines of statistics, Vol II : Goon Guptha, M.K.Guptha, Das Guptha B.

3. Introduction to Mathematical Statistics : Hoel P.G. 15

Practicals Semester – IV

Conduct any 6 (Ms-exel is compulsory)

1.Large sample tests for mean(s).

2. Large sample tests for proportion(s). 3. Large sample tests for standard deviation(s).

4.Large sample tests for Fisher's Z- transformation.

5.Small sample tests for Single and Doublet-test.

6.Small sample tests for Paired t-test.

7.F-Test.

8. Chi square test for independence of attributes.

9. Non-parametric tests – run test.

10. Non-parametric tests - median test.

11 Non-parametric tests - sign tests.

12.MS-Excel methods for the above Serial Numbers 1,2,3,4.(any one of above)

KAKARAPARTI BHAVANARAYANA COLLEGE (AUTONOMOUS)(Sponsored by S.K.P.V.V.Hindu High Schools’ Committee)

Kothapeta, Vijayawada(An Autonomous College in the Jurisdiction of Krishna University)

ISO-9001-2008 CERTIFIED INSTITUTION NAAC ‘A’ GRADESTATISTICS INFERENCE

SEMESTER-IV

MODEL PAPERSECTION-A

Answer any five of the following 5x5=25

1. Explain consistency2. Explain one and two tailed tests3. If T is an unbiased estimator Ɵ. Show that T2 is a biased estimator forƟ24. Explain critical region and level of significane5. Explain procedure for testing of hypothesis6. Explain paired t-test for difference of means7. Explain test of significance for single mean8. Advantages of NP tsestsSECTION-B

Answer all the following 5x10=50

9. a) Explain method of moments in estimation(or)b) If X is a poisson variate with parameters λ. Find the maximumlikelihood estimate of λ on the basis of a size n10. a) State and prove N-P lemma(or)b) a sample of size 1 is taken from poisson(Ɵ). Let H0: Ɵ =1against H1:Ɵ=2. Consider the test function ɸ(x) ={ 1 for x>30 otherwiseFind the probabilities of the type I and type II errors.11.a) Explain the test of significance for difference of means and itsconfidence limits. (or)b) In a year there are 956 births in a town a of which 52.5% weremales.while in town a and b combined this proportion in a total of1406 births was 0.496. Is there any significant difference in theproportion of male births in two towns?12.a) Explain chi-square test for goodness of fit(or)b)The time taken by workers in performing a job by method I andmethod II is given belowmethod I: 20 16 26 27 23 22method II: 27 33 42 35 32 34 38

Do the data show that the variables of time distribution from

Population from which these samples are drawn do not differ signficant

13.a) Explain two sample median test

(or)

b) Explain sign test for paired sample

KAKARAPARTI BHAVANARAYANA COLLEGE (AUTONOMOUS)(Sponsored by S.K.P.V.V.Hindu High Schools’ Committee)

Kothapeta, Vijayawada(An Autonomous College in the Jurisdiction of Krishna University)

ISO-9001-2008 CERTIFIED INSTITUTION NAAC B++ (80-85 GRADE POINTS)STATISTICS STT501 2012-2013 B.Sc .MSCs

W.e.f:2012-13SEMESTER –V SYLLABUS PAPER-5

APPLIED STATISTICS-IObjectives

the aim of this course is to have the knowledge of time series data and components,index numbers and predicting prices and quantities change.Learning outcomes

1. Understand the concept of time series and its components, measres for eliminatingtrend and seasonal variations

2. Understand the concept of vital statistics, methods of collecting it. And measures offertility and mortality

Unit-I:Time-SeriesTime-Series and its components with illustrations, additive, multiplicative models.Determination of trend by least squares, Moving average methods, Determination ofseasonal indices by Ratio to moving average, Ratio to trend and link relative method.

Unit-II: Index NumbersConcept, construction, uses and limitations of simple and Weighted Index numbers,

Lasperyers, Paashce’s and Fisher’s Index numbers. Criterion of a good Index number.Fisher’s Index number is an Ideal Index number. Fixed and chain based Index number,

cost of living Index number and whole-sale Price Index number. Base shifting, Splicingand deflation of Index number.

Unit-III: Vital Statistics:Definition and uses of Vital Statistics. Sources of Vital Statistics: Registration method

and census method. Rates and Ratio’s, Mortality rates: Crude death rate, Age specific deathrate general fertility rat, total fertility rate. Measurement of population growth: Crude rate ofnatural Increase, Pearle’s Vital Statistics. Gross reproduction rate and Net reproduction rate,life table construction and uses of life tables and Abridge life tables.

Unit-IV: Official Statistics and Excel:Functions and organization of CSO and NSSO. Agricultural statistics, Area and Yield

statistics.Using Formulas and functions : Entering & Editing formulas, (Statistical only) using

range names and Labelsin formulas manipulating data with worksheet functions, testingand debugging formulas, creating and editing charts; building an excel chart, selecting datato plot, selecting a chart type, choosing a standard chart type, creating and saving customchart types.

List of Reference Books:

-1. Fundamentals of Applied Statistics by S.C.Gupta & V.K. Kapoor2. Applied Statistics: Primal Mukhopadhyay, New Book Agency.3. Indian Official Statistics: M.R.Saluja: ISI publications.4. Pratirupa Sidhanthamulu: Telugu Academy5. Statistical Methods: S.P..Gupta, Sultan chand company.6. Statistics Made simple: K.V.S. Sarma (P.H.I)

BLUE PRINT

SEMESTER-V APPLIED STATISTICS-II (STT 501) PAPER-VSection-A Marks-75

Answer all the Questions. All Questions carry equal marks

i.e.; 4x10=40M

Section-B

5 Questions answered out of 8 Questions

Each Question carries 5 marks

i.e.; 5x5=25M

Section-C

5 Questions must be Answered.

Each Question carries 2 marks

i.e.; 5x2=10M

Section-A +Section-B+ Section-C

40 + 25 + 10 = 75Marks

WeightageUNIT- Topic LAQ SAQ VSAQ

I Time Series 2 2 1

II Index Numbers 2 2 2

III Vital Statistics 2 2 1

IV Official Statistics & Demand

Analysis 2 2 1

KAKARAPARTI BHAVANARAYANA COLLEGE (AUTONOMOUS)(Sponsored by S.K.P.V.V.Hindu High Schools’ Committee)

Kothapeta, Vijayawada(An Autonomous College in the Jurisdiction of KrishnaUniversity)

ISO-9001-2008 CERTIFIED INSTITUTION NAAC B++ (80-85 GRADE POINTS)STATISTICS STT501 2012-2013 B.Sc .MSCs

W.e.f:2012-13SEMESTER –V Model Paper PAPER-5

APPLIED STATISTICS-IITime : 3hrs SECTION -A Marks:75

Answer any FOUR of the following Questions 4x10=40M

1. Define Time-Series? What are the components of Time-Series.(Or)

Explain Ratio to trend method for measuring seasonal Variations.

2. What is an Index number. Discuss the problems involved in the construction of an Indexnumber.

(Or)Explain cost of living Index number. Write the steps involved in the construction of thecost of living Index number.

3. Discuss Various measures of fertility rates.(Or)

Define Complete life table. What are Various components of complete life table.4. Explain various functions of C.S.O

(Or)Define the following terms

i. Statistical functions in Excel.ii. Explain creating charts in Excel.

SECTION -BAnswer any FIVE of the following 5x5=25M

5. Explain the Additive and Multiplicative model of time Series.6. Write Semi-average method for measuring trend in a time series.7. Explain Whole-Sale price Index number.8. Explain Base shifting and Splicing.9. Write any two methods of measuring Mortality rates.10. Describe various sources of Vital Statistical data.11. Briefly Explain Creation of custom chart?12. Write the functions of N.S.S.O.

SECTION -CAnswer the following Questions 5x2=10M

13. Uses of time series.

14. Formulae of Laasperyers and Paasches Index number.

15. Abridge life table.

16. Time reversal & factor reversal test

17. Explain work sheet.

KAKARAPARTI BHAVANARAYANA COLLEGE (AUTONOMOUS)(Sponsored by S.K.P.V.V.Hindu High Schools’ Committee)

Kothapeta, Vijayawada(An Autonomous College in the Jurisdiction of Krishna University)

ISO-9001-2008 CERTIFIED INSTITUTION NAAC B++ (80-85 GRADE POINTS)STATISTICS STT502 2012-2013 B.Sc .MSCs

W.e.f:2012-13SEMESTER –V SYLLABUS PAPER-6

OPERATION RESEARCH-IObjectives

The aim of this course is to provide knowledge about OR formulation and solvingindustrial problems.Learning outcomes

1. Understand the concept of formulation of LPP problems and finding solution forindustrial problems.

2. Understand the concept of transportation and solving problems minimizing the cost.

Unit-I: Introduction to Operation Research

The origin and the development of OR, the nature and definition of OR, objective of OR,Scope of OR, characteristic of OR, Applications of OR.

Unit-II: Linear Programming Problem

Definition of Linear programming Problem, formulation of LPP, Solution of LPP byGraphical method. Simplex algorithm, concept of Artificial variables. Big-M (PenaltyMethod).

Unit-III: TransportationProblems

Definition of Transportation problem, Transportation problem as a special case of LPP,feasible solutions by North-West corner Rule, Matrix minima method, Row minimamethod, Column minima method and Vogel’s Approximation method. Optimal solutionthrough MODI tableau method. Transhipment.

Unit-IV: Assignment and sequencing Problems

Formulation and description of Assignment problem. Minimisation and maximisationUnbalanced Assignment problem, Travelling salesman problem. Optimum solutionusing Hungarian method. Problems of sequencing, optimum sequence of N jobs on 2machines and 3 machines.

Text Book: -

Operation Research: Kanti Swaroop,P.K.Gupta & Man Mohan ,Sultan Chand & Sons

List of References: -

1. S.D.Sarma: Operation Research, Meerut Publications2. Dr.R.K.Gupta: Operation Research, Krishna prakashan Media(p) Ltd, Meerut.3. Hadly: Linear programming, Addiosn-weslesy.

BLUE PRINT

SEMESTER-V Operation Research-I (STT 502) PAPER-VI

Section-A Marks-75

Answer all the Questions. All Questions carry equal marks

i.e.; 4x10=40M

Section-B

5 Questions answered out of 8 Questions

Each Question carries 5 marks

i.e.; 5x5=25M

Section-C

5 Questions must be Answered.

Each Question carries 2 marks

i.e.; 5x2=10M

Section-A +Section-B+ Section-C

40 + 25 + 10 = 75Marks

UNIT Topic LAQ SAQ VSAQ

I Introduction to OR 2 2 --

II Linear Programming problem 2 2 3

III Transportation Problem 2 2 1

IV Assignment and Sequencing

Problem 2 2 1

KAKARAPARTI BHAVANARAYANA COLLEGE (AUTONOMOUS)(Sponsored by S.K.P.V.V.Hindu High Schools’ Committee)

Kothapeta, Vijayawada(An Autonomous College in the Jurisdiction of KrishnaUniversity)

ISO-9001-2008 CERTIFIED INSTITUTION NAAC B++ (80-85 GRADE POINTS)STATISTICS STT502 2012-2013 B.Sc .MSCs

W.e.f:2012-13SEMESTER –V Model Paper PAPER-6

OPERATION RESEARCH-ITime: 3hrs SECTION -A Marks:75

Answer any FOUR of the following Questions 4x10=40M1.(a) Define Operation Research? Write the Aim and Scope of Operation Research.

(or)(b) What is OR? What are the applications of OR.2. (a) Explain the procedure of Simplex Algorithm.

(or)(b) Solve the following LPP by Simplex method.

Maximize Z= 3x1+2x2Subject to constraints 2x1+x2 ≤ 2

3x1+4x2 ≤ 12 and x1, x2 ≥ 0.3.(a) Explain MODI method of transportation.

(or)(b) Using Vogels method find IBFS of the transportation.

Problem where cost matrix is given below.A B C D Availability

EFG

111621

131824

171413

141010

250300400

4.(a) Requirement: Solve the following Assignment ProblemMachines

Jobs

(or)4.(b) Solve the following Sequencing Problem.

1 2 3 4 512345

948417436

2278284211

5872912757

1150374922

1963453925

Task: 1 2 3 4 5 6 7Machine I: 3 12 15 6 10 11 9Machine II: 8 10 10 6 12 1 3

SECTION -BAnswer any FIVE of the following 5x5=25M

5. Write the Characteristic of OR.6. What are the objectives of OR.7. Write the Graphical Procedure of an LPP.8. Solve the given LPP by graphical Procedure.Maximize Z = 2x1+3x2

Subject to constraints x1-x2 ≤ 2x1+x2 ≥ 4 and x1, x2 ≥ 0.

9. Write the procedure of North-West Corner Rule.10. Transportation problem is special case of LPP .Discuss11. Write the procedure of ‘n’ jobs 2-machines.12. Explain formulation and Description of an Assignment Problem.

SECTION -CAnswer the following Questions 5x2=10M

13. What is OR.14. Formulation of an LPP.15. Define transportation Problem.16. Basic feasible solution.17. Transhipment.

KAKARAPARTI BHAVANARAYANA COLLEGE (AUTONOMOUS)(Sponsored by S.K.P.V.V.Hindu High Schools’ Committee)

Kothapeta, Vijayawada(An Autonomous College in the Jurisdiction of Krishna University)

ISO-9001-2008 CERTIFIED INSTITUTION NAAC B++ (80-85 GRADE POINTS)STATISTICS STT601 2012-2013 B.Sc .MSCs

W.e.f:2012-13SEMESTER –VI SYLLABUS PAPER-7

APPLIED STATISTICS-IIObjectives

The aim of this course is to provide knowledge about sampling methods and samplesurveys, design of experiments.Learning outcomes

1. Understand the concept of sampling, methods of drawing a sample, methods ofcollection of primary data

2. Understand the concept of design of experiments one way variation and two sidedvariation. Solving the real life problems

Unit-I: Design of Sample SurveysConcept of Population, Sample, Sampling Unit, Parameter, Statistic, Sampling

distribution, standard error principal steps in sample surveys - need for sampling, censusversus sample surveys.

Sampling and Non-sampling Errors, sources and treatment of non-sampling Errors,advantages and limitations of sampling.Types of Sampling: Subjective, probability and mixed sampling methods. Methods ofdrawing random samples with and without replacement. Estimates of population mean,total and proportions their variances and estimates of variances the following methods.

i) SRSWR and SRSWOR.ii) Stratified random sampling with Proportional and Neymann allocation.

Comparison relative efficiencies.iii) Concept of Systematic sampling. (No derivation for systematic sampling).

Unit-II-: Analysis of VarianceIntroduction of ANOVA, one-way classification with one observation per cell -

concept of Gauss Markov Linear model. Statement of Cochran’s theorem fixed effectmodel, random effect model. Expectation of sum of squares. Statistical model ofANOVA,ANOVA table. Two-way classification of ANOVA mathematical, Statisticalmodel of ANOVA.

Unit-III: Design of Experiments-I.Introduction, principles of an Experimental Design; Randomization, Replication,

Local control, Completely Randomized Design (CRD) - Advantages, DisadvantagesMathematical Analysis and statistical analysis. Lay out.

Unit-IV: Design of Experiments-II.Lay out of Randomized Block Design, Advantages & Disadvantages statistical

and Mathematical Analysis. Efficiency of R.B.D compared to CRD. Latin square designlay out Advantages and Disadvantages, statistical and mathematical analysis of LSD.

Books Reference: -1. Theory and Analysis of sample survey designs by Daroga Singh and chowdary.2. Fundamentals of Applied Statistics by SC.Gupta& V.K. Kapoor.3. AnuvartitaSankhyakaSastram - Telugu Academy.4. Basic statistics. New age Publications - B.C.Agarwal.5. Comprehensive Statistical methods - S.Chand by AroraSumeetArrora.

BLUE PRINT

SEMESTER-VI APPLIED STATISTICS-II(STT 601) PAPER-VISection-A Marks-75

Answer all the Questions. All Questions carry equal marks

i.e.; 4x10=40M

Section-B

5 Questions answered out of 8 Questions

Each Question carries 5 marks

i.e.; 5x5=25M

Section-C

5 Questions must be Answered.

Each Question carries 2 marks

i.e.; 5x2=10M

Section-A +Section-B+ Section-C

40 + 25 + 10 = 75Marks

UNIT-I Topic LAQ SAQ VSAQ

I Design of Sample surveys 2 2 1

II Analysis of Variance 2 2 2

III Design of Experiment-I 2 2 1

IV Design of Experiment-II 2 2 1

KAKARAPARTI BHAVANARAYANA COLLEGE (AUTONOMOUS)(Sponsored by S.K.P.V.V.Hindu High Schools’ Committee)

Kothapeta, Vijayawada(An Autonomous College in the Jurisdiction of KrishnaUniversity)

ISO-9001-2008 CERTIFIED INSTITUTION NAAC B++ (80-85 GRADE POINTS)STATISTICS STT601 2012-2013 B.Sc .MSCs

W.e.f:2012-13SEMESTER –VI Model Paper PAPER-7

APPLIED STATISTICS-IITime : 3hrs SECTION -A Marks:75

Answer any FOUR of the following Questions 4x10=40M

1. In SRSWOR, show that the Variance of the sample mean is given by Var (yn) = S2 N-nnN

(or)What are the types of sampling techniques and Explain.

2. ExplainANOVA one - way classification.(or)

Explain ANOVA Two - way classification.3. What are the principles of Design Experiments.

(or)What are the Advantages and Disadvantages of CRD give its applications.

4. Describe the analysis of Randomized Block Design.(or)

What is LSD? And write the analysis of LSD?

SECTION -BAnswer any FIVE of the following 5x5=25M

5. What are the different sources of Errors in Sample Survey.

6. In Neymann allocation, show that ni∝NiSi.

7. What is ANOVA? What are the Assumptions.

8. What is the difference between variability with in classes and variability between the

classes? Explain with suitable example.

9. Write the Lay-out of LSD

10. Comparison between RBD and LSD.

11. What are the limitations of Sampling?

12. Describe the advantages of stratified random sampling.

SECTION -CAnswer the following Questions 5x2=10M

13. Comparison between systematic sampling and simple random sampling.14. Standard error.15. Replication16. Experimental error17. Precision

List of Practicals

Practical-III StatisticsPractical (STT 601P) -III

1. Measurement of trend by method of Least-Squares and Moving Averages.

2. Determination of Seasonal Indices by Moving Averages and Ratio to trend method. And

Link relative.

3. Measurement of trend by method of Least-Squares and Moving Averages using MS-

Excel.

4. Determination of Seasonal Indices by method of Ratio to Moving Averages, Ratio to

trend and Link relative using MS- Excel.

5. Simple Random sampling with and without Replacement SRSWR, SRSWOR.

6. Stratified Random sampling with Proportional and optimum allocations.

7. ANOVA one - way classification with equal number of observations.

8. ANOVA one - way classification with equal number of observations by MS-Excel.

9. ANOVA Two - way classification with equal number of observations.

10. ANOVA Two - way classification with equal number of observationsby MS-Excel

11. Analysis of CRD with out Missing observation.

12. Analysis of CRD with out Missing observation by MS-Excel.

13. Analysis of RBD with out Missing observation.

14. Analysis of RBD with out Missing observation by MS-Excel.

15. Analysis of LSD with out Missing observation.

16. Analysis of LSD with out Missing observation by MS-Excel.

17. Computation of Simple and weighted Index numbers.

18. Computation of Reversal test.

19. Computation of Cost of living Index numbers.

20. Computation of Various mortality rates and Reproduction rates.

21. Construction of Life-tables.

KAKARAPARTI BHAVANARAYANA COLLEGE (AUTONOMOUS)(Sponsored by S.K.P.V.V.Hindu High Schools’ Committee)

Kothapeta, Vijayawada(An Autonomous College in the Jurisdiction of KrishnaUniversity)

ISO-9001-2008 CERTIFIED INSTITUTION NAAC B++ (80-85 GRADE POINTS)STATISTICS STT602 2012-2013 B.Sc .MSCs

W.e.f:2012-13SEMESTER –VI SYLLABUS PAPER-8

OPERATION RESEARCH-IIObjectives

The aim of this course is to provide knowledge about quality control anddetermining various charts, network analysis.

Learning outcomes:

1. Understand the concept of quality control different types of charts, attribute charts fordefectives and defects.

2. Understand the concept of games optimal and mixed strategy. Construction ofnetwork analysis

Unit-I: Statistical Process ControlImportance of SQC in Industry, Statistical basis of Stewart Control charts, construction ofcontrol charts for variables - Mean, Range, Standard deviation charts.

Unit-II: Control Charts for AttributesP chart, np Chart and C-Chart. Interpretation of control charts. Natural tolerance limits

and specification limits. Concept of six sigma and its importance.Differences between control charts for Variables and Attributes.

Unit-III: Game theoryIntroduction, Characteristics of Game theory, Basic Definitions - Maximin, Minimax,

criterion, Saddle point, optimal strategies and value of game, solution of 2x2 gameproblem, Algebric method, Dominance Property, graphical Procedure. Statement ofImportance of fundamental theorem of games. Elements of Pure and mixed Strategies.Game problems as a special case of linear programming problem.

Unit-IV: Network AnalysisBasic concepts of Project schedule network analysis. Construction of the Network

diagram.CPM/PERT techniques.Critical Path method.Determination of Critical path.The project Evaluation and review technique (PERT).

Reference Books: -1. Applied statistics - S.C.Gupta, V.K.Kapoor.

2.Operation Research - S.D.Sharma.

BLUE PRINT

SEMESTER-V Operation Research-I (STT 602) PAPER-VI

Section-A Marks-75

Answer all the Questions. All Questions carry equal marks

i.e.; 4x10=40M

Section-B

5 Questions answered out of 8 Questions

Each Question carries 5 marks

i.e.; 5x5=25M

Section-C

5 Questions must be Answered.

Each Question carries 2 marks

i.e.; 5x2=10M

Section-A +Section-B+ Section-C

40 + 25 + 10 = 75Marks

UNIT Topic LAQ SAQ VSAQ

I Statistical Process control 2 2 --

II Control Chart for Attributes 2 2 3

III Game theory 2 2 1

IV Network Analysis 2 2 1

KAKARAPARTI BHAVANARAYANA COLLEGE (AUTONOMOUS)(Sponsored by S.K.P.V.V.Hindu High Schools’ Committee)

Kothapeta, Vijayawada(An Autonomous College in the Jurisdiction of KrishnaUniversity)

ISO-9001-2008 CERTIFIED INSTITUTION NAAC B++ (80-85 GRADE POINTS)STATISTICS STT602 2012-2013 B.Sc .MSCs

W.e.f:2012-13SEMESTER –VI Model Paper PAPER-8

OPERATION RESEARCH-IITime : 3hrs SECTION -A Marks:75

Answer any FOUR of the following Questions 4x10=40M

1.(a) Define SQC? What are the factors influence of SQC?(or)

(b) Write the procedure of construction of control charts.2.(a) Explain the construction of np chart.

(or)(b) Explain (i) Natural tolerance limits and (ii) specification limits.

3. (a) Solve the following game by using Graphical method.Player B

B1 B2 B3 B4player A A1 1 0 3 2

A2 2 1 0 -2(b) Explain two person zero sum game, pure strategy, mixed strategy.

4. (a) State the objectives of CPM and write algorithm on it.(b) Write the Rules to construct Net Work diagram.

SECTION -BAnswer any FIVE of the following 5x5=25M1. What are the uses of SQC.2. Uses of C-Chart3. Write the Dominance property of game theory.4. 3 − control limits.5. Properties of Net- Work6. Explain the construction of Mean-chart.7. Explain Min- max Max-mini principal .8. Explain the characteristics of PERT/CPM.

SECTION -CAnswer the following Questions 5X2=10M

1. Write process control.2. Define game theory.3. Expand PERT/CPM.4. Saddle point5. Control limits of Mean chart.

List of Practicals

Practical-IVStatisticsPractical -IV (STT 602P)

1. Formulation of LPP Graphical solution (using different inequality type constraints)2. Solution of LPP by Simplex method.3. Solution of LPP by Big-M method.4. Formulation and solution of transportation problem using N-W method, Matrix minima

and VAM5. Transportation problem by MODI method.6. Formulation and solution of assignment problem using Hungarian method.7. Solution of Unbalanced Assignment problem.8. Solution of Sequencing Problem.

i. Processing ‘n’ Jobs through two machines.ii. Processing ‘n’ Jobs through three machines.

9. Construction of Mean, Range and standard deviation charts.10. Construction of P,np and C chart.11. To construct of network diagram, identify critical path and calculation of latest time of

earliest times.12. Game theory: i) Dominance property

ii) Graphical Procedure.