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Code No: 13141

VIKRMA SIMHAPURI UNIVERSITY : NELLORE

FIRST B.A / B.Sc. – STATISTICS

PAPER – I : DESCRIPTIVE STATISTICS AND PROBABILITY DISTRIBUTIONS

(WITH MATHS COMBINATION)

UNIT – I

Descriptive Statistics: Moments, Central and non-central 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 examples. 15L

Probability: Basic concepts in probability: Deterministic and random experiments, trail, outcome,

sample space, event, and operations of events mutually exclusive and exhaustive events and

equally likely and favorable outcomes with examples. Mathematical, statistical and axiomatic

definitions of probability with merits and demerits. Properties of probability based on axiomatic

definition. Conditional probability and independence of events. Addition and multiplication

theorems for n events. Boole’s inequality and Baye’s theorem. Problems on probability using

counting methods and theorems. 15L

UNIT – II

Random variables: Definition of random variable, discrete and continuous random variables,

functions of random variables, probability density function with illustrations. Distribution function

and its properties. Notion of bivariate random variable, bivariate distribution and statement of its

properties. Joint, marginal and conditional distributions. Independence of random variables. 15 L

Mathematical Expectation: Mathematical expectation of a function of a random variable. Raw

and central moments and covariance using mathematical expectation with examples. Addition and

multiplication theorems of expectation, Definition of moment generating function (m.g.f),

cumulant generating function (c.g.f), and characteristic function (c.f) and statements of their

properties with applications. Chebyshev’s , and Cauchy-Schwartz’s inequalities. 15 L

UNIT-III

Discrete distributions: Binomial, Poisson, Negative binomial, Geometric and Hyper-

geometric(mean and variance only) distributions. Properties of these distributions such as m.g.f

,c.g.f., c.f., and moments up to fourth order and their real life applications. Reproductive property

wherever exists. Binomial approximation to Hyper-geometric, Poisson approximation to Binomial

and Negative binomial distributions. 30L

UNIT – IV

Continuous distributions: Rectangular and Normal distributions, Normal distribution as a limiting

case of Binomial and Poisson distributions. Exponential, Gamma and Beta of two kinds (mean and

variance only) distributions. Properties of these distributions such as m.g.f., c.g.f., c.f., and

moments upto fourth order, their real life applications and reproductive productive property

wherever exists. 30L

List of reference books:

1. V.K.Kapoor and S.C.Gupta: Fundamentals of Mathematical Statistics, Sultan

Chand & Sons, New Delhi.

2. Statistics Paper – I (Telugu Academy, Hyderabad)

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

4. Goon AM, Gupta MK, Das Gupta B : Fundamentals of Statistics , Vol-I, the World Press

Pvt.Ltd., Kolakota.

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

6. M. JaganMohan Rao and Papa Rao: A Text book of Statistics Paper-I.

7. Sanjay Arora and Bansi Lal: New Mathematical Statistics: Satya Prakashan , New Delhi

8. Hogg Tanis Rao: Probability and Statistical Inference. 7th

edition. Pearson

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

Instructions to the Paper Setter

1. Since each question carry only 10 Marks, simple questions with sufficient clarity is to be

set in the question paper.

2. Since there is a separate practical examination, higher focus should be on theoretical

concepts than numerical problems.

3. The following table reveals the distribution of questions for each unit and in each topic

Unit Topic

No. of

questions

to be set

UNIT - I

1. Moments, Skewness & Kurtosis

2. Probability

3 2

UNIT - II

1. Discrete random Variable

2.Continuous random variable

3. Mathematical expectation

4. Generating functions

5. Inequalities

1 1 1 1 1

UNIT – III

1. Binomial Distribution

2. Poisson Distribution

3. Negative Binomial Distribution

4. Geometric Distribution

5. Hyper Geometric Distribution

1 1 1 1 1

UNIT – IV

1. Uniform, Gamma and Beta distributions

2. Exponential Distribution

3. Normal Distribution

2 1 2

Code No:13141

MODEL QUESTION PAPER

STATISTICS

(With Mathematics Combination)

Common to B.A / B.Sc

Paper-I: Descriptive Statistics and probability distributions

Time: 3hours Max.Marks:100

Note: 1. Answer any TEN questions choosing atleast one from each unit

2. Each question carry 10 Marks

UNIT - I

1. Define raw moments and central moments. Derive an expression to express central moments

in terms of raw moments

2. For a frequency distribution, show that (i) 2 1 (ii) 2 1

3. Define skewness. State its properties and measures.

4. State and prove addition theorem on probability for ‘n’ events

5. State and prove Baye’s Theorem.

UNIT - II

6. Define distribution function of a random variable and state its properties

7. The following the p.d.f. of a random variable (1 ); 0 1

( )0

kx x xf x

otherwise

Find k and P (0.2<x<0.6)

8. State and prove addition theorem on expectation

9. Define cumulant generating function. Derive relations between moments and cumulants.

10. State and prove chebychev’s inequality

UNIT - III

11. With usual notations, in binomial distribution, show that 1r = pq 1r

d rnr

dp

12. Derive Poisson as the limiting case of binomial distribution

13. Define negative binomial distributions. Derive its m.g.f. and hence find its mean and variance

14. Show that geometric distribution lacks memory in a certain sense

15. Define hyper geometric distribution. Find its mean and variance

UNIT - IV

16. Derive the mean deviation about mean for rectangular distribution

17. Define exponential distribution. Find its m.g.f and hence its mean and variance

18. Define normal distribution. Write down the properties of normal curve.

19. For normal distribution, show that QD: MD : SD = 10 : 12 : 15.

20. Define Gamma Distribution and find its mean and variance.

Practical – Paper 1

List of Practical

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

6. Pearson’s coefficient of skewness.

7. Bowley coefficient of skewness.

8. Skewness based on moments and Kurtosis

9. Fitting of Binomial distribution – Direct Method

10. Fitting of Binomial distribution – Recurrence relation

11. Fitting of Poisson distribution – Direct Method

12. Fitting of Poisson distribution – Recurrence relation

13. Fitting of negative binomial distribution

14. Fitting of geometric distribution

15. Fitting of normal distribution – Ordinates method

16. Fitting of normal distribution –Areas method

17. Fitting of exponential distribution

Note : The above practical problems may be worked through Ms Excel also

Statistics Practical Examinations

Time: 3hrs Max.marks: 50

Five questions to be set from the following topics and three to be answered.

Record – 10 Marks; 3 x 13 = 39 + 1 (for impression)

Topic No. of questions

to be set

Central tendency, Dispersion,

Moments, Skewness, Kurosis 1

Binomial, Geometric

distributions 1

Poisson, Negative, Binomial

distributions 1

Normal distribution 1

Exponential distribution 1

Total 5

Code No :23141

B .A/B.Sc. II Year: Statistics Syllabus


Paper - II: Statistical Methods and Inference

Unit – I

Population correlation coefficient and its properties. Bivariate data, scatter diagram, sample

correlation coefficient, computation of correlation coefficient for grouped data.

Spearman’s rank correlation coefficient and its properties. Principle of least squares, simple linear

regression, correlation verses regression, properties of regression coefficients. Fitting of quadratic

and power curves. Analysis of categorical data, independence and association and partial

association of attributes, various measures of association (Yule’s) for two way data and coefficient

of contingency (Pearson and Tcherprow), coefficient of colligation. (30L)

Unit – II

Concepts of population, parameter, random sample, statistic, sampling distribution and standard

error. Standard error of sample mean(s) and sample proportion(s). Exact sampling distributions,

Statement and properties of 2, t and F distributions

Point estimation of a parameter, concept of bias and mean square error of an

estimate. Criteria of good estimator- consistency, unbiasedness, efficiency and

sufficiency with examples. Estimation by method of moments, Maximum likelihood

(ML), statements of asymptotic properties of MLE. Concept of interval estimation.

Confidence intervals of the parameters of normal population (30 L)

Unit –III

Concepts of statistical hypotheses, null and alternative hypothesis, critical region, two types of

errors, level of significance and power of a test. One and two tailed tests, Neymann - Pearson’s

fundamental lemma for Randomized tests. Examples in case of Binomial, Poisson, Exponential

and Normal distributions. Large sample tests and confidence intervals for mean(s), proportion(s),

standard deviation(s) and correlation coefficient(s).

(30 L)

120 hrs (4 hrs/ week)

Unit – IV

Tests of significance based on 2, t and F. 2-test for goodness of fit and test for independence of

attributes .Non-parametric tests- their advantages and disadvantages, comparison with parametric

tests. Measurement scale- nominal, ordinal, interval and ratio. Run Test, Sign and Median

test(Both one sample and two Samples Tests) (30 L)

List of Reference Books:

1. V.K.Kapoor and S.C.Gupta: Fundamentals of Mathematical Statistics, Sultan

Chand&Sons, New Delhi

2. Statistics Paper-II (Telugu Academy, Hyderabad

3. Goon AM, Gupta MK,Das Gupta B : Outlines of Statistics , Vol-II, the World Press

Pvt.Ltd., Kolkota.

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

5. Sanjay Arora and Bansi Lal: New Mathematical Statistics Satya Prakashan , New Delhi

6. Hogg and Craig : Introduction to Mathematical statistics. Printis Hall

7. Siegal,S. and Sidney: Non-parametric statistics for Behavioral Science. McGraw Hill.

8. GibbonsJ.D and Subhabrata Chakraborti: Nonparametric Statistical Inference. Marcel Dekker.

9. Parimal Mukhopadhyay: Mathematical Statistics. New Central Book agency.

10. Conover : Practical Nonparametric Statistics. Wiley series.

11. V.K.Rohatgi and A.K.Md.Ehsanes Saleh: An introduction to probability and statistics. Wiley

series.

12. Mood AM,Graybill FA,Boe’s DC Introduction to theory of statistics. TMH

13. K.V.S. Sarma: Statistics made simple do it yourself on PC. PHI

14. Gerald Keller: Applied Statistics with Microsoft excel. Duxbury. Thomson Learning

15. Levin, Stephan, Krehbiel, Berenson: Statistics for Managers using Microsoft Excel.4th

edition.

Pearson Publication.

16. Hogg, Tanis, Rao Probability and Statistical Inference. 7th

edition Pearson Publication.

Instructions to the Paper setter






Unit Topic No. of Questions to

be set

UNIT-I

1.Curve fitting

2.Correlation

3.Rank Correlation

4. Regression

5.Theory of Attributes

1

1

1

1

1

UNIT-II

1.Preliminaries of Estimation

2. t, F, 2 Distributions (p.d.f. & properties)

3.Theory of estimation

1

1

3

UNIT-III

1. Preliminaries of testing of hypothesis

2. N.P. Lemma and its applications

3.Large sample tests

1

2

2

UNIT-IV

1.t-tests

2. 2 -tests

3. F-Test

4. N.P. Tests

1

1

1

2

Code No :23141

Model Question Paper

Statistics (With Mathematics Combination)

Common to B.A / B.Sc

Paper-II - Statistical Methods and Inference

Time : 3hours Max. marks: 100

Note: 1. Answer any TEN questions choosing at least ONE from each unit.

2. Each question carries 10 marks.

Unit-I

1. Derive normal equations fit a second degree parabola.

2. Define correlation coefficient and prove that -1<r<+1

3. Derive the limits for rank correlation coefficient

4. Derive the regression line of Y and X

5. Define Yule’s coefficient of association and coefficient of colligation and establish a

relation between them.

Unit - II

6. Define the following terms with examples

a) Population b) Sample c) Parameter d) Statistic

7. Define t-distribution Mention its properties and uses.

8. Explain the properties of a good estimate.

9. In normal distribution show that both sample mean square co-efficient and sample

variance are consistent estimators for population variance.

10. Derive a maximum likelyhood estimator for the parameter in exponential

distribution.

Unit - III

11. Explain the following terms

a) Two types of Errors. b) Critical region c) Power of the test.

12. Sate and prove Neymann - Pearson Lemma.

13. By Using N.P. Lemma, find the best critical region for testing 0 0 1 1: ( ) :H vs H

on the basis of sample drawn from a Poisson population.

14. Explain the large sample test to examine the significant difference between two sample

means.

15. Explain the test to examine the population correlation coefficient in large samples.

Unit - IV

16. Explain the –test for independence of attributes.

17. Explain paired t-test.

18. Explain the F-test for the significant difference between two sample variances.

19. Explain run test.

20. Explain median test.

List of Practical’s

1. Fitting of straight line

2. Fitting of second degree parabola.

3. Fitting of exponential curve of I Kind

4. Fitting of exponential curves of II Kind

5. Fitting of power curve

6. Computation of correlation coefficient

7. Computation of correlation coefficient – Bivariate data

8. Rank correlation coefficient.

9. Fitting of Regression lines

10. Computation of coefficient of association and Colligation

11. Computation of Contingency coefficients.

12. a) Test for Population Mean.

b) Test for the significant difference between two sample means.

13. a) Test for Population Standard deviations.

b) Test for the significant difference between two sample Standard deviation.

14. a) Test for Population Proportion.

b) Test for the significant difference between two sample Proportions.

15. a) Test for population correlation coefficient

b) Test for the significant difference between two sample correlation coefficient.

16. t- test for Population Mean.

17. t- test for the significant difference between two sample means.

18. Paired T-Test

19. Chi- Square test for goodness of fit - Binomial Distribution.

20. Chi- Square test for goodness of fit - Poisson Distribution

21. Chi- Square test for independence of attributes.

22. Test for the significant difference between two sample variances.

23. Run Test.

24. Sign Test.

25. Median Test.


B.A/B.Sc. II Year: Statistics Syllabus


(Examination at the end of II Year)

Practical Paper – II

Time :3 Hours Max. Marks:50


Record – 10 marks 3 X 13 = 39 + 1 (for impression)

Topic No. of Questions to be set

Curve fitting 1

Correlation, Rank Correlation,

Regression, Attributes

1

Large Sample Tests 1

Small Sample Tests 1

Non Parametric Tests 1

Total 5

90 hrs (3 hrs/ week)

Code No:33141

VIKRAM SIMHAPURI UNIVERSITY:NELLORE

Paper III – Applied Statistics

(With Maths Combination)

Common to BA/B.Sc 90hrs (3hrs / week)

Unit-I

Design of sample surveys:

Concept of population, sample, sampling unit, parameter, statistic, sampling errors, sampling

distribution, sampling frame and Standard Error. Principal steps in sample surveys, need for

sampling, census versus sampling.

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 of drawing

random samples with and without replacement. Estimation of population mean, total and

proportion, their variances

i) SRSWR AND SRSWOR

ii) Stratified random sampling with proportional and Neymann allocation and

iii) Systematic sampling when N = nk comparison of relative efficiencies. Advantages and

Disadvantages of above methods of sampling.

Unit-II

Analysis of Variance: One-way and Two-way classification with one observation per cell.

Expectation of various sum of squares, mathematical analysis and applications to design of

experiments.

Design of Experiments:

Principles of experimentation, analysis of completely randomised design (CRD), Randomised

block design (RBD) and Latin square design (LSD) including one missing observation.

Unit-III

Time series: Time series and its components with illustrations, additive, multiplicative models.

Determination of trend by least squares (Linear trend, parabolic trend only), moving average

method, simple average method. Determination of seasonal indices by Ratio to trend and Link

relative methods.

Index Numbers

Concept, Construction, uses and limitations of simple and weighted index numbers. Laspayer’s,

Paasche’s and Fisher’s index numbers, Criterion of good index number, problems involved in the

construction of index numbers. Fisher’s ideal index numbers. Fixed and chain base index numbers

cost of living index number and wholesale price index number. Base shifting, splicing and

deflation of index numbers.(6L)

Unit-IV

Official Statistics: Functions and organization of CSO and NSSO. National income and its

computation.

Vital Statistics: Introduction, definition and uses of vital statistics, sources of vital statistics,

Registration method and census method. Rates and ratios, crude death rate, age specific death rate,

standardised death rate, crude birth rate, age specific fertility rate, general fertility rate, total

fertility rate, measurement of population growth, crude rate of natural increase, pearl’s vital index.

Gross reproduction rate and net reproduction rate. life tables, construction and uses of life tables,

abridged life tables.

LIST OF REFERENCE BOOKS

1. V.K.KAPOOR AND S.C.Gupta: Fundamentals of applied statistics. Sultan Chand.

2. Statistics-Paper III (Telugu Academy, Hyderabad)

3. M.R.Saluja: Indian official statistics. ISI publications.

4. B.L.Agarwal: Basic Statistics, new age publications.

5. S.P.Guptha: Statistical methods. Sulthan Chand & sons.

6. K.V.S.Sarma:Statistics made simple: Do it yourself on PC.PHI

7. Arora,Sumeet Arora,S.Arora: comprehensive statistical methods. S.Chand.

8. Statistics:Theory & methods-B.N.Guptha.

Instructions to the Paper Setter






Unit Topic No. of

question is to be set

1.Design of sample

Surveys

1. Theoretical concepts of sampling.

2. SRSWOR & SRSWR

3.Estimate of stratified random sampling

4.Proportional and optimal allocation methods.

5. Systematic random sampling.

1

1

1

1

1

II. Analysis of

Variance and

Design of

Experiments

1. ANOVA one way and two way classifications.

2. Necessity and principles of experimentation

3. CRD

4.RBD

5.LSD

1

1

1

1

1

III. Time series

&index numbers.

1. Concept of time series.

2. Estimation of trend.

3. Determination of seasonal indices.

4. Index numbers.

1

1

1

2

IV. Official

Statistics and Vital

Statistics.

1. Functions and organization of CSO and NSSO

2. Computation and utility of national income.

3. Concepts of vital statistics

4.Different vital rates.

5. Life table.

1

1

1

1

1

Code No:33141


Statistics (With Maths Combination)

Common to BA/B.Sc

Paper-III: Applied Statistics

Time 3 Hrs Max marks:100

Note: 1. Answer any Ten questions choosing atleast one from each unit.

2. Each question caries 10 Marks.

Unit-I

1. Explain the main steps involved in planning and execution of sample survey.

2. In SRSWOR, Show that 2( )N n

V y SNn

3. Define stratified random sampling. Bring out its advantages over simple random sampling.

4. With usual notations, show that ( )ran prop opt ststV y V y V y

5. Define systematic random sampling. With usual notations, show that

22

11sys wsy

k nNV y S

N NS

Unit-II

6. Explain one way classification by brining the assumptions involved in it.

7. Explain the principles of experimentation with suitable examples.

8. Write down the statistical analysis of randomized block design.

9. Describe latin square design, Write down its layout.

10. Define missing plot in experimental designs. Derive the expression to estimate the

missing plot in an R.B.D.

Unit-III

11. Explain various components involved in time series analysis.

12. Explain the least square method to estimate the trend in time series analysis.

13. Explain the method of link relatives to estimate the seasonal indices in time series analysis.

14. Define Index Number, Explain various weighted index numbers.

15. Explain the procedure to construct the cost of living index number. Also bring out its uses

and limitations.

Unit - IV

16. Explain the main functions of central statistical organization.

17. Explain computational procedure of National income.

18. Define the rate of mortality. Explain various death rates in vital statistics and write the

merits and demerits.

19. Explain various rates of fertility and write the merits and demerits.

20. Explain the columns of a life table.

Paper-III: List of Practicals

1. Simple random sampling without replacement – Estimation of population means, variance

and total.

2. Simple random sampling with replacement – Estimation of population means, variance and

total.

3. Stratified random sampling - Proportional & Optimal allocation method.

4. Systematic random sampling - Estimation of population mean and variance.

5. One way classification - ANOVA

6. Two way classification - ANOVA

7. Analysis of CRD.

8. Analysis of RBD.

9. Analysis of RBD with one missing plot.

10. Analysis of LSD.

11. Analysis of LSD with one is missing Plot.

12. Measurement of Trend - Method of moving averages.

13. Measurement of Trend - Straight line.

14. Measurement of Trend - Second degree parabola.

15. Determination of seasonal indices - Ratio to trend method.

16. Determination of seasonal indices - Method of link relatives.

17. Computation of simple index numbers.

18. Computation of weighted index number.

19. Reversal test

20. Construction of cost of living index number.

21. Computation of various mortality rates.

22. Construction of life table.

23. Computation of various fertility rates.

24. Computation of gross and reproduction rates.


Statistics Practical Examination



Record - 10 marks; 3 x 13 = 39 + 1 (for impression).

Topic No. of questions

to be set

Sampling 1

ANOVA & Designs 1

Time Series 1

Index Numbers 1

Vital Statistics 1

Total 5

Code No:43141

VIKRAM SIMHAPURI UNIVERSITY:NELLORE

PAPER-IV: Quality, Reliability and Operations Research

(with Maths Combination)

Common to B.A / B.Sc 90hrs (3hrs / weak)

Unit-I

Statistical Process Control:

Importance of SQC in industry, Statistical basis of shewart control charts. Construction of control

charts for variables (mean, range and standard deviation) and attributes (pnp and c-charts with

fixed and varying sample sizes). Interpretation of control charts, Natural tolerance limits and

specification limits.(20L)

Unit-II

Acceptance sampling plans: Procedures risk and consumer’s risk and their OC and ASN

functions. Design of single and Double sampling plans for attributes using Binomial.

Reliability: Introduction failure rates, Hazard function, instantaneous failure rates, mean time

between failures, estimation of reliability, exponential distribution as life model, its memory less

property. (20L)

Unit-III

Linear programming: Meaning and scope of OR, Definition of general LPP, Formulation of LPP,

Solution of LPP by graphical method, simplex algorithm, concept of artificial variable, Big-M

method. (25L)

Unit-IV

Transportation, Assignment and Sequencing problems: Definition of transportation problem,

TPP as special case of LPP, feasible solution by north west corner rule, least cost method and

VAM for balanced and unbalanced transportation problem. Formulation and Description of

assignment problem, assignment problem as special case of TP and LPP, unbalanced assignment

problem, travelling sales person problem, optimal solution using Hungarian method.

Problem of sequencing: Optimal sequence of n jobs on two and three machines without

passing.(25L)

List of reference books

1.Kanti swaroop, P.K.Guptha and Man Mohan: Operation Research. Sultan Chand.

2.V.K.Kapoor and S.C.Gupta: Fundamentals of Applied Statistics. Sultan Chand.

3.Statistics – Paper IV (Telugu Academy, Hyderabad).

4.S.K Sinha: Reliability and life testing. Wiley Eastern.

5.R.C.Gupta: Statistical Quality Control.

INSTUCTIONS TO THE PAPER SETTER

1. Since each question carry only 10 marks, simple questions with sufficient clarity is to be set

in the question paper.

2. The ratio of theory and problems should be 60% to 40%.It means 8 numerical applications

should be set among the total 20 questions

3. While setting a numerical problem as a 10 marks question in the question paper , the

working time for the problem should not exceed 10 to 15 minutes for an average student.

For example,

Simplex method: 2 variables, 3 constants

3 variables, 2 constants.

Transportation : Should not exceed 3 rows & 4 columns or 4 rows & 3 columns

Assignment : Should not exceed 5X5 matrix

Sequencing : Should not exceed 6 jobs.

4. The following table reveals the distribution of questions for each unit in each topic.

Unit Topic No. of questions to be set

1.Statistical

process control

II. Acceptance

sampling plans

reliability

III. Linear

Programming

IV. Transportation,

Assignment and

sequencing

problem.

1.Importance, Statistical basis of SQC

2.Variable control charts

3.Attribute control charts

4.Tolerance limits and specification limits.

5. Numerical application.

1.Producer’s risk & consumer’s risk.

2.AQL and LTPD

3.Single sampling plan

4.Double Sampling plan

5.Reliability.

1.Meaning and scope

2.Formation of LPP

3.Graphical solution to LPP

4.Simplex method, type-I inequalities

5.Big-M-method

1.Transportation balanced problem

2.Transportation-unbalanced problem

3.Assignment problem

4.Sequencing:n jobs-2 machines

5.Sequencing :n jobs-3 machines

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

Code No : 43141


Statistics Syllabus

(With Maths Combination)

Common to BA/B.Sc

Paper-IV: Quality, Reliability and Operations Research


Note: 1.Answer any Ten questions choosing at least one from each unit.

2. Each question caries 10 Marks.

Unit-I

1. What do you understand by statistical quality control? Discuss briefly its need and utility in

industry.

2. Explain in detail the construction of x and R charts. Also write down its applications.

3. Explain the statistical basis and procedure to construct P-Chart. Also explain its application

method.

4. Distinguish between defect and defective. Explain how to construct c-Chart by brining the

statistical basis involved in it.

5. Explain the difference between specification limits, tolerance limits and control limits in

SQC.

Unit-II

6. What do you understand by acceptance sampling plan. State its uses by giving illustrations.

7. Describe single sampling plan and OC, AOQ curve for this plan.

8. Distinguish clearly between (i) Producer’s Risk and consumer’s risks ii) AQL and LTPD.

9. Define double sampling inspection plan. Bring out its merits and demerits over a single

sampling inspection plan.

10. Define reliability. Explain the importance of hazard function in the computation failure

rate.

Unit-III

11. Define linear programming problem. Explain the role of slack, surplus and artificial

variables in solving linear programming problems.

12. A company has three operational departments with capacity to produce three different types

of cloths yielding a profit of Rs.2 Rs.4 and Rs.3 per meter respectively. One meter of

suiting require 3 minutes in weaving 2 minutes in processing and 1 minute in packing. One

meter of woollen requires 3 minutes in each department. In a week, total run time of each

department is 60,40 and 80 hours for weaving, processing packing respectively. Formulate

the above as linear programming problem.

13. Solve the following LPP graphically

Maximize 1 2Z = 4 + 3 x

Subject to the Constraints

1 2

1 2

1 2

1 2

2 x + x = 1000

x + x = 800

x = 400 and x = 700

and x 0x

14. Solve the following LPP simplex method

Maximize. 1 2Z = 4 x + 10 x

Subject to the constraints

1 2

1 2

1 2

1 2

2 x +x 50

2 x + 5 x 100

2 x +3 x 90

x 0 and x 0

15. Use penalty method

Maximize. Z=6x1+4x2.

Subject to the constraints.

1 2

1 2

1 2

1 2

2 x +3 x 30

3 x +2 x 24

x + x 3

x 0 and x 0

Unit - IV

16. Write down in transportation problem in the form of LPP. Explain any one method to find

the IBFS of a transportation problem.

17. Find the IBFS of the following transportation problem using VAM.

Factory

Ware House Capacity

D E F G

A 42 48 38 37 160

B 40 49 52 51 150

C 39 38 40 43 190

Demand 80 90 110 160

18. Solve the following assignment problem using Hungarian algorithm.

8 7 9 10

7 9 9 8

10 8 7 11

10 6 8 7

w x y z

a

b

c

d

19. Define a sequencing problem. Explain the assumptions involved in a sequencing problem.

20. In a factory there are six jobs to perform, each of which should go through two machines A

and B in the order A, B. The processing timings ( in hours) for the jobs are given here. You

are required to determine the sequence for performing the jobs that would minimize. The

total elapsed time is T. What is the value of T.

Job J1 J2 J3 J4 J5 J6

Machine A 1 3 8 5 6 3

Machine B 5 6 3 2 2 10

Paper-IV

List of Practicals.

1. Construction of( x ,R) charts-Mean and standard deviation unknown.

2. Construction of ( x ,R) charts-Mean and standard deviation unknown.

3. Construction of P-chart-Fixed sample size.

4. Construction of P-Chart –Variable sample size.

5. Construction of np-Chart.

6. Construction of c-Chart.

7. Single sampling plan –OC curve.

8. Reliability Measures

9. LPP- Graphical solution.

10. LPP-Simplex method.(Maximization)

11. LPP-Simplex method.(Minimization)

12. LPP- Big M method.

13. IBFS of transportation problem- North-West corner method.

14. IBFS of transportation problem –Least Cost Method.

15. IBFS of transportation problem-Vogel’s approximation method.

16. Assignment Problem (Balanced).

17. Assignment Problem (Unbalanced).

18. Travelling sales person problem.

19. n jobs-2 machines sequencing problem.

20. n jobs-3 machine sequencing problem.


Statistics Practical Examination-IV


Five questions to be set from the following topics and three to be answered

Record-10 marks; 3x13=39+1(for impression)

Topic No. of questions to be set

SQC 1

OC Curves 1

OR (LPP) 1

Transportation Problem 1

Assessment and Sequencing Problem 1

Total 5

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