Download B.Sc./B.A. I STATISTICS PAPER - I PROBABILITY THEORY (paper

B.Sc./B.A. I
STATISTICS
PAPER - I
PROBABILITY THEORY (paper code - 0803)
UNIT I
Concepts of probability, defination of Probability, Classical and Priory probability, limitations of mathematical
probability, Statistical/ Empirical probability and its limitations, Axiomatic approach of probability, Random
Experiment: Trial, sample point and sample space, definition of an event, operation of events, mutually
exclusive and exhaustive events. Discrete sample space, properties of
Probability based on axiomatic approach.
UNIT II
Some theorems on Probability: Addition theorem, extension of Addition theorem for n events, Booles’s
Inequality, Conditional Probability, Multiplication theorem of probability, Independence of events.
Multiplication theorem of probability for independent events. Bayes’ theorem and its applications.
UNIT III
Random Variables: Definition of discrete random variables, probability mass function, Discrete distribution
function, various measures of central tendency, dispersion, Skewness and Kurtosis for continuous probability
distributions. Uniform & Binomial distributions.
UNIT IV
Expectation of a random variable and its properties ( Addition theorem & Multiplication theorem), Properties of
variance, Covarience, variance of a Linear Combination of random variables, moments of Bivariate
Probability distributions, Conditional expectations and conditional variance.
UNIT V
Short Notes based on above four units, one from each unit. Answer any two of four.
REFERENCES:
1. Bhat B.R., Srivenkatramana T and Rao Madhava K.S. (1997): Statistics: A Beachner's Text, Vol. II new
Age International (P) Ltd.
2. Edward P.J. Ford J.S. and Lin (1974): Porbability for statistical decision- Making, Prentice Hall.
3. Goon A.M. Gupta M.K., Das Gupta.B. (1999): Fundamentals of statistics, Vol World Press Calcutta.
4. Gupta, S.C. and Kapoor, V.K. (2011): Fundamentals of Mathematical Statistics, Vol I, Sultan Chand &
Sons.
5. Mood A.M. Grabill F.A. and Boes D.C. (1974): Introduction to the theory of statistics, Mc Graw Hill.
ADDITIONAL REFERENCES:
1.
2.
3.
4.
C ooke, Cramer and Clarke (): Basic Statistical computing, Champan and Hall.
Devid S. (1996): Elementary Probability, Oxford Press.
Hoel P.G. (1971): Introduction to Mathematical Statistics, Asia Publishing House
Meyer P.L. (1970): Introductory Probability and Statistical applications. AddisionWesley
PAPER - II
DESCIRIPTIVE STATISTICS (paper code - 0804)
UNIT I
Type of Data: Concepts of population and sample in Statistics, qualitative and quantitative data. Homogeneous/
heterogeneous data, Nominal and Ordinal data, Cross sectional and time series data, discrete and continuous
data, nominal, ordinal, ratio and interval scales. Collection of data: Primary data- designing a questionnaire and
a schedule, Secondary data- sources of data, government publications, and recorded data. Complete
enumeration, controlled experiments, observational studies and sample survey, Editing of Statistical Data.
UNIT II
Presentation of Data: classification and tabulation of data. Diagrammatic and graphical representation of data.
Frequency distributions, cumulative frequency distributions and their graphical representation. Histogram,
frequency polygon and Ogive, Stem and leaf char and Box plot. Numerical examples for plotting graphs.
Analysis of Quantitative Data: Univariate data, Concepts of Central tendency or location, Dispersion and
relative Dispersion, Skewness and Kurtosis, and their measures. Numerical examples based for calculating
Central tendency, Dispersion, Skewness and Kurtosis.
UNIT III
Bivariate Data: Scatter diagram. Correlation Coefficient and its properties. Coefficient of determination.
Correlation Ratio and Regression. Principle of least squares. Fitting of linear regression and related results.
Multiple correlation and Partial Correlation for three variables. Numerical examples based on Correlation,
Multiple correlation and Partial Correlation for three variables and Regression lines.
UNIT IV
Standard Continuous distributions- Normal distributions, p.d.f. of Normal distribution, Special characteristics
of Normal distribution moments, Moment generation function, cumulant generating function and characteristics
function of Normal distribution, Fitting of Normal distribution. Rectangular distribution, moments and m.g.f.
and characteristic function of Rectangular distribution.
UNIT V
Short notes based on all above four units, one from each unit. Answer any two.
REFERENCES:
1. Bhat B.R. Srivenkairamana T and Rao Madhava K.S. (1996): Statistics: A Beginner's Text, Vol. I, New
Age International (P) Ltd.
2. Croxion F.E. Covden D.J. and kelin S (1973): Applied General Statistics, Prentice Hall of Inida.
3. Goon A.M. Gupta M.K.,Das Gupta. B. (1991): Fundamentals of Statistics, Vol. I, World Press, Calcutta.
4. Gupta, S.C. and Kapoor, V.K. (2011): Fundamentals of Mathematical Statistics, Vol. I, Sultan Chand &
Sons.
ADDITIONAL REFERENCES:
1.
2.
3.
4.
Anderson T.W. and Sclove S.L (19718) An Introduction to the Statistical Analysis of. Houghton Miffin\Co.
Cooke, Cramer and Clarke (): Basic Statistical Computing, Chapman and Hall.
Mood A.M, Graybill F.A. and Boes D.C. (1974): Introduction to the Theory of Sttistics,
Mc Graw Hill. Snedecor G.W. and Cochian, W.G. (1976): Statistical Mehtods. Lowa State University
Press.
5. Spiegel, M.R. (1967): Theory & Problems of Statistics, Schaum's Publishing Series.
PAPER – III PRACTICAL
1.
2.
3.
4.
5.
6.
7.
8.
Presentation of data by Frequency tables, diagrams and graphs.
Calculation of Measures of central tendency, dispersion, skewness and Kurtosis:
Correlation, multiple & Partial correlation coefficient
Fitting of Curves by the least square method.
Regression of two variables.
Multiple correlation and Partial correlation.
Exercises on measures of central tendency
Dispersion, skewness and Kurtosis .
B.Sc. /B.A. II
STATISTICS
PAPER - I (Paper Code - 0853)
STATISTICAL METHODS
UNIT-I
Census and Sampling Investigation, universe or population, Census Inquiry, sample Inquiry. Sampling Method,
difference between Census & sampling objects of sampling, precision in sampling, random sampling, stratified
sampling, sample size, test of reliability of sampling, bias in sampling. Random sample. Sampling distribution
of Binomial, Poisson and Normal distributions.
UNIT II
Theory of Attributes, order of classes and class frequencies, Relation between class frequencies, consistency of
data, conditions of consistency of data, Independence of attributes, criterion of Independence, Association of
Attributes, Yule’s Coefficient of Association, Coefficient of colligation. Numerical examples based on
Association and independence of attributes.
UNIT III
Exact Sampling Distribution: Definition of Chi-square distribution and its p.d.f (without derivation),
Application of Chi-square distribution, Inference about a population variance, Pearson's chi-square test for
goodness of fit and chi-square test for homogeneity of correlation coefficient. Yates’ correction for 2x2
contingency table. Numerical examples based on Chi-square.
UNIT IV
Large Sample Test: Students’ - t, and F statistics. Applications of t-test, F-test and Fisher's Z transformation
and its applications. Numerical examples based on Students’ - t, and F statistics.
UNIT V
Four short notes, one from each unit . Students have to answer any two.
REFERENCES 1. Freund, J.E. (2001) : Mathematical Statistics, Prentice Hall of India.
2. Goon A.M., Gupta M.K., Das Gupta B. (1991) : Fundamentals of Statistics, Vol. I, World Press, Calcutta.
3. Hodges J.L. and Lehman E.L. (1964) : Basic Concepts of Probability and Statistics, Holden Day.
4. Mood A.M., Graybill F.A. and Boes D.C. (1974) : Introduction to the Theory of Statistics, McGraw Hill.
ADDITIONAL REFERENCES :
1. Bhat B.R. Srivenkatramana T and Rao Madhava K.S. (1997) : Statistics : A Beginner'sText, Vol. II, New
Age International (P) Ltd.
2. Rohatgi V.K. (1967) : An Introduction to Probability Theory and Mathematical Statistics, John Wiley &
Sons.
3. Snedecor G.W. and Cochran W.G. (1967) : Statistical Methods. Lowa State University Press.
PAPER - II (Paper Code - 0854)
A - SAMPLE SURVEY
UNIT-I
Design of Sample Surveys, parameter and Statistics, sampling distribution, standard errors, utility of standard
error, principle step in sample survey, principle of sample survey, sampling and non-sampling errors advantage
of sampling over complete census, limitations of sampling. Types of Sampling: Subjective or Judgement
sampling, Probability sampling, mixed sampling. Simple random sampling (with and without replacement),
Merits and limitations of Simple random sampling.
UNIT-II
Stratified random sampling, Systematic sampling, systematic sampling, cluster sampling, multistage sampling
and sequential sampling (without derivations & theorems)), Advantages of these methods of sampling.
B – ANALYSIS AND DESIGN OF EXPERIMENTS
UNIT-III
Definition of Analysis of variance (ANOVA), uses of analysis of variance, assumption of analysis of variance,
Mathematical model and Analysis table of ANOVA in one way classifications and ANOVA in two-way
classifications. Numerical examples based on the topics.
UNIT-IV
Fundamental principles of design experiments, Treatment, experimental units, blocks, experimental errors,
replication, precision, efficiency of design, randomization, replication and local control in experimental design.
Randomized block design (RBD)- layout, advantages, disadvantages, statistical analysis for one observation per
experimental unit and applications. Completely randomized Design (CRD) - layout, advantages,
disadvantages, statistical analysis for one observation per experimental unit, applications. Numerical examples
based on the topics.
UNIT V
Short notes based on above four units, one from each unit. Answer any two out of the four.
REFERENCES:
1. Das M.N. and Giri (1986) : Design and Analysis of Experiments, Springer Verlag.
2. Des Raj (2000) : Sample Survey Theory, Narosa Publishing House.
3. Gupta, S.C. & Kapoor, V.K.: Fundamentals of Applied Statistics. Vol. II, Sultan Chand &
Sons.
4. Murthy M.N. (1967) : Sampling Theory and Methods, Statistical Publishing Society, Calcutta.
5. Sampath S. (2000) : Sampling Theory and Methods, Narosa Publishing House.
6. Sukhatme B.V. (1984) : Sample Survey Method and its Applications, Indian Society of
Agricultural Statistics.
7. Goon A.M., Gupta M.K., Das Gupta B. (1986) : Fundamentals of Statistics, Vol.II, World Press,
Calcutta.
PAPER – III
PRACTICAL
Practical based on Paper I and Paper II
Paper I- Numerical examples based on each UNIT.
Paper II- Numerical examples based on each UNIT
B.Sc. /B.A. III
PAPER-I (Paper Code-0907)
APPLIED STATISTICS
UNIT-I
Indian Official Statistics : Present official statistical system in India, Methods of collection of official statistics,
their reliability and limitations, and the principal publications containing such statistics on the topicspopulation agriculture, industry, trade, price, labour and employment, transport and communications, banking
and Finance.
UNIT-II
Demographic Methods : meaning and uses of Vital Statistics, sources of data, Measures of mortality, crude
death rates, specific death rate, age specific death rate,standardized death rate, infant mortality rates, death date
by cause, standardized death rate, complete life table - its main features, mortality rate and probability of dying,
use of survival tables. Measurement of fertility - crude birth rate, general fertility rate, specific fertility rate, age
specific fertility rate, total fertility rate, gross reproduction rate, net reproduction rate. Numerical examples
based on the topics.
UNIT-III
Statistical law of Demand and Supply: Law of supply and demand, price elasticity of demand significance of
elasticity of demand, demand function with constant price elasticity, price elasticity of supply, types of data
require for estimating elasticities, Leontief Method,Pigous method,Engel law and Engel’s curve,Parato’s law of
Income distribution. Numerical examples based on the topics.
UNIT-IV
Time SeriesAnalysis: Components of time series, Analysis of time series, uses of time series, measurement
trend, method of curve by least square method, second degree curve fitting, moving average method,
measurement of seasonal fluctuations, ratio to trend method, ratio to moving average method. Numerical
examples based on the topics.
UNIT-V
Short notes based on above four units, one from each unit.. Answer any two out of the four.
REFERENCES:
1. Goon, A.M., Gupta, M.K., Das gupta, B (1986) : Fundamentals of statistics, vol.-II, World Press, Calcutta.
2. Gupta, S.C. & Kapoor : Fundamentals of Applied Statistics. Vol. II, Sultan Chand & Sons.
3. Guide to Current Indian Offical Statistics : Central Statistical Organization, Govt. of India, New Delhi.
4. Saluja M.P. ( ) Indian Official statistical Systems, Statistical Publishing Society, Calcutta.
5. Srivastava, O.S. (1983) : A textbook of Demography, Vikas Publishing.
ADDITIONAL REFERENCES:
1. Gupta and Mukhopadhyay P.P. ( ) Aplied Statistics, Central Book Agency.
2. Pressat R. (1978) : Statistical Demography, Methuen and Co. Ltd. B.Sc.-III (39)
PAPER-II
(Paper Code-0908)
STATISTICAL QUALITY CONTROL AND COMPUTATIONAL TECHNIQUES
UNIT-I
Importance of statistical methods in industrial research and practice, chance and assignable cause,uses of SQC,
Process and product control, control charts, 3-sigma control charts, control Charts for variables, construction of
X- bar and R charts, control charts for attributes, np, p and c charts. Numerical examples based on the topics.
UNIT-II
Computational Techniques - definition and applications of index numbers, classification of Index number,
price and quatity index number,base period, calculation of index number- simple aggregate method, weighted
average method, Laspeyre's, Paasche's and Fisher's ideal index numbers. Averages of Price Relatives, Chain
indices, . Criteria for good Index numbers, Time reversal test, factor reversal test. Consumer Price Index.
Numerical examples based on the topics.
UNIT III
Numerical Analysis : Finite Difference tables and methods of interpolation and extrapolation , Gregory
Newton's forward interpolation formula for equal intervals, Gregory Newton's backward interpolation formula
for equal intervals, Newton's divided difference formula, and Lagrange's methods of interpolation for unequal
intervals. Numerical examples based on the topics.
UNIT-IV
Linear Programming : Quantitative approach to decision making, history of operations research, models and
model building , examples of LP model in operations research, advantage of operations research study,
operations research models in practice. Linear Programming: application and model formulation, graphical
solution methods of linear programming problems, unboundedness, infeasible solution, degeneracy ,
redundancy. Examples of marketing, finance, agriculture and product mix problems. Standard form of LPP,
Simplex method of solution of linear programming problems.
Numerical examples based on the topics.
UNIT-V
Four short notes, one from each unit. Student have to answer any two.
REFERENCES:
1. Brownless K.A. (1960) : Statistical theory and Methodology in Science and Engineering. John Wiley and
Sons.
2. Grant E.L. (1964) : Statistical Quality Control, McGraw Hill.
3. Duncan A.J. (1974) : Quality Control and Industrial Statistics, Traporewala and Sons.
4. Gass S.I. (1975) : Linear Programming Methods and Applications, McGraw Hill.
5. Rajaraman, V. (1981) : Computer Oriented Numerical Methods, Prentice Hall.
6. Sastry S.S. (1987) : Introductory Methods of Numerical Analysis, Prentice Hall.
7. Taha H.A. (1989) : Operations Research : An Introduction, Macmillan Publishing Company.
ADDITIONAL REFERENCES:
1. Bowker H.A. and Liberman G.T. (1962) : Engineering Statistics, Prentice Hall.
2. Cowden D.J. (1960) : Statistical Methods in Quality Control, Asia Publishing Society.
3. Garvin W.W. (1960) : Introduction to Linear Programming, McGraw Hill.
4. Mahajan M. (2001) : Statistical Quality Control, Dhanpat Rai & Co. (P) Ltd.
5. Rao S.S. (1984) : Optimization Theory and Applications, Wiley Eastern. B.Sc.-III (40)
6. Krishnamurthy E.V. and Sen S.K. (1976) : Computer Based Numerical Algorithms, Affiliated
East-West Press.
PAPER – III PRACTICAL
Practical based on Paper I and Paper II
Paper I- Numerical examples based on each UNIT.
Paper II- Numerical examples based on each UNIT
1.
2.
3.
4.
Computing measures of mortality & fertility,
Construction of Index Numbers by Laspeyre's, Paasche's, Fisher's method.
Determination of trend in a time series, construction of seasonal indices.
Fitting of Pareto curve to income data, Lorenz curve of concentration, Estimation of price elasticity of
demand form time series data.
5. Drawing of X-R, np, p and c- charts. Drawing of OC curve for single and double sampling plans for
attributes, AOQ and ATI curves
6. Construction of difference tables, use of Newton's Lagrange's methods of interpolation and divided
difference formulae,
7. Formulation of LPP's and their duals. Solving LPPs by graphical and simplex methods.