MIDNAPORE COLLEGE (AUTONOMUS) SYLLABUS FOR B.Sc. STATISTICS (HONOURS) UG_STAT_HONS 1 Department of Statistics Course Structure of B.Sc. Statistics 20% marks are allotted for internal assessment of each theoretical paper and 20% marks are allotted for note-book and viva-voice of each practical paper Semester Paper Code Group Paper Name Full Marks I 101 A Probability Theory-I 25 B Real Analysis and Numerical Methods 25 102 Descriptive Statistics-I 25 103 Practical based on Paper 101-B( Numerical Methods) & 102 25 Total 100 II 201 A Probability Theory-II 30 B Population Statistics 20 202 A Descriptive Statistics-II 25 B Official & Economic Statistics and Time Series analysis 25 203 Practical based on Paper 201-A(Fitting of distribution & Scalling), 201-B & 202 50 Total 150 III 301 A Probability Theory-III 20 B Linear Algebra 30 302 A Statistical Computing in C 25 B Multivariate Analysis 25 303 A Practical based on Paper 302-A 25 B Practical based on Paper 301-B & 302-B 25 Total 150 IV 401 A Sampling Distribution & Statistical Inference-I 35 B Statistical Quality control 15 402 A Large Sample Theory 15 B Sample Survey Methods 35 403 Practical based on Paper 401 & 402 50 Total 150
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MIDNAPORE COLLEGE (AUTONOMUS) SYLLABUS FOR B.Sc. STATISTICS (HONOURS)
UG_STAT_HONS 1
Department of Statistics
Course Structure of B.Sc. Statistics
20% marks are allotted for internal assessment of each theoretical paper and 20% marks are allotted for note-book and viva-voice of each practical paper
Semester Paper
Code Group Paper Name
Full
Marks
I
101 A Probability Theory-I 25
B Real Analysis and Numerical Methods 25
102 Descriptive Statistics-I 25
103 Practical based on Paper 101-B( Numerical Methods) & 102
25
Total 100
II
201 A Probability Theory-II 30
B Population Statistics 20
202 A Descriptive Statistics-II 25
B Official & Economic Statistics and Time Series analysis
25
203 Practical based on Paper 201-A(Fitting of distribution & Scalling), 201-B & 202
50
Total 150
III
301 A Probability Theory-III 20
B Linear Algebra 30
302 A Statistical Computing in C 25
B Multivariate Analysis 25
303 A Practical based on Paper 302-A 25
B Practical based on Paper 301-B & 302-B 25
Total 150
IV
401 A Sampling Distribution & Statistical Inference-I 35
B Statistical Quality control 15
402 A Large Sample Theory 15
B Sample Survey Methods 35
403 Practical based on Paper 401 & 402 50
Total 150
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Semester Paper
Code Group Paper Name
Full
Marks
V
501 A Statistical Inference-II 25
B Linear Models & Design of Experiments-I 25
502 Practical based on Paper 501 50
503 Practical based on Statistical Computing (in Excel & R)
50
Total 150
VI
601 A Statistical Inference-II 20
B Design of Experiments-II 30
602 A Practical based on Paper 601 25
B Project 25
Total 100
Total 800
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Semester-I
(101-A) Probability Theory-I (25 marks)
Random experiment: Trial, sample point, sample space and events, different operations
on events. Definitions of probability: Subjective and objective probability, Classical, empirical, and Kolmogorov’s axiomatic (detailed discussion on discrete space only). Relative-frequency approach (long run) to probability. Limitations of classical and empirical definitions of probability. Examples based on classical definition of probability and repeated trials. Theorems on probability of events. Probabilities of union and intersection of events, Probabilities of exactly m and at least m among n (> m) events. Sequences of events and their limits; Continuity of probability measures. Conditional probability and independence of events, Bayes’ theorem and its applications. Illustrations using difference equation (1st order only), product space and independent trials, Geometric probability. References:
1. Chung K.L. (1983): Elementary Probability Theory with Stochastic Process, Springer / Narosa
2. Feller W. (1968): An Introduction to Probability Theory & its Applications, John Wiley 3. Goon A.M., Gupta M.K. & Dasgupta B. (1994): An Outline of Statistical Theory (Vol-1),
World Press 4. Rohatgi V.K. (1984): An Intro. to Probability Theory & Math. Statistics, John Wiley 5. Hoel P.J., Port S.C. & Stone C.J. ( ): Introduction to Probability Theory (Vol-1), Mifflin &
UBS 6. Cramer H. (1954): The Elements of Probability Theory, John Wiley 7. Parzen E. (1972): Modern Probability Theory and its Applications, John Wiley 8. Uspensky J.V. (1937): Introduction to Mathematical Probability,McGraw Hill 9. Cacoullos T. (1973): Exercises in Probability. Narosa 10. Rahman N.A. (1983): Practical Exercises in Probability and Statistics, Griffen 11. Pitman J. (1993): Probability, Narosa 12. Stirzaker D. (1994): Elementary Probability, Cambridge University Press 13. Chandra T.K. & Chatterjee D. (2001): A First Course in Probability, Narosa 14. Bhat B.R. (1999): Modern Probability Theory, New Age International 15. Rohatgi VK & Saleh: An Introduction to Probability and statistics 16. Goon AM & Roy D: Problems in probability theory 17. Mukhopadhaya P: Mathematical Statistics
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(101-B) Real Analysis & Numerical Methods (25 marks)
Real Analysis
Elementary set theory, finite, countable and uncountable sets, supremum, infimum. Sequences, monotone sequences, limit of sum and product of sequences, series of numbers, simple test of convergence, power series, absolute convergence, limsup, liminf. Continuity and its different characterization, uniform continuity, types of discontinuities, intermediate value theorem, absolute continuity. Differentiability, MVT, L’Hospital rule, Taylor’s theorem, statement of Taylor’s theorem for several variables, extrema of functions (with or without constraints). Sequences and series of functions, uniform convergence. Riemann sums and Riemann integral, Improper Integrals, Gamma and Beta integrals, integration by parts, change of variable formula Multiple integral and Jacobian (without proof). Functions of several variables, directional derivative, partial derivative, and derivative as a linear transformation, inverse and implicit function theorems. Concepts of o and O, Polar and Orthogonal transformations. References:
1. Apostol T.M. (1985): Mathematical Analysis, Narosa 2. Apostol T.M. (1968): Calculus ( Vols 1 & 2) 3. Goldberg R.R. (1953): Methods of Real Analysis, Oxford & IBH Pub. Co. 4. Widder D.V. (1994): Advanced Calculus 5. Piskunov N. (1977): Calculus ( Vols 1 & 2 ) 6. Malik S.C. & Arora S.(1991): Mathematical analysis 7. Narayan S. (1984): A course of Mathematical Analysis, S.Chand & Company Ltd. 8. Bartle R.G. and Sherbert D.R (third edition): Introduction to Real Analysis. 9. Malik SC: Principles of real analysis 10. Mapa SK: Real Analysis 11. Chakraborty A: Real analysis (Vol-1&2)
Numerical Methods
Approximation of numbers and functions, absolute and relative errors. Operators: Δ, , E and divide difference and properties.
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Interpolation: Polynomial approximation, Difference Table, Newton’s Forward, Backward and divided difference interpolation formulae and Lagrange’s general interpolation formula, Error terms, Inverse interpolation. Numerical differentiation and its applications. Numerical integration: Trapezoidal & Simpson’s 1/3 rd and 3/8th rule, Euler-maclaurin’s sum formula. Numerical solution of equations: method of bisection and regular false. Method of fixed point iteration and Newton-Raphson method in one unknown, Conditions of convergence, rates of convergence and geometrical interpretation of each method. Extension of the iteration method to two unknowns (without convergence). Stirling’s approximation to factorial n References :
Introduction: Nature of Statistics, Population and sample, Uses and abuses of Statistics, Statistics and other disciplines. Types of data: Primary and secondary data, Qualitative and quantitative data, Nominal, ordinal and cardinal data. Cross-sectional and time-series data, Discrete and continuous data, Frequency and non-frequency data. Different types of scale of measurement: Nominal, Ordinal, Ratio and interval. Collection and scrutiny of data: Collection of primary data-direct observation method. Interview method, mailed questionnaire method, Types of schedules and questionnaires and their designing, Data from controlled experiments. Scrutiny of data for internal consistency and detection of errors in recording, Ideas of cross validation. Presentation of data: Construction of tables with one or more factors of classification, Diagrammatic presentations of non-frequency data. Construction of frequency distributions and cumulative frequency distributions and their graphical and diagrammatic presentations. Stem and leaf displays. Analysis of quantified data: Univariate data -Different characteristics of frequency distributions with their measures including quintiles: central tendency (including Trimmed
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and Winsorised mean), dispersion and relative dispersion of grouped and ungrouped data, moments including Sheppard's corrections (without derivation), skewness and kurtosis, Box plot, Outlier Detection. References :
1. Goon A.M.,Gupta M. K., Dasgupta B.(1998): Fundamentals of Statistics (V-1),World Press 2. Yule G.U & Kendall M.G. (1950): An Introduction to the Theory of Statistics, C.Griffin 3. Snedecor & Cochran (1967): Statistical Methods (6thed), Iowa State Univ. Press 4. Croxton F.E., Cowden D.J. & Klein (1969): Applied General Statistics, Prentice Hall 5. Wallis F.E. & Roberts H.V. (1957): Statistics- a new approach, Methuen 6. Tukey J.W. (1977): Exploratory Data Analysis, Addison-Wesley Publishing Co.
103 Practical (25 marks)
Practical problem based on paper 101-B (Numerical Methods) and 102 (Descriptive
Statistics I).
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Semester – II
(201-A) Probability Theory II (30 marks)
Random Variables : Definition of discrete and continuous random variables, probability
mass function (p.m.f.) and probability density function (p.d.f.), cumulative distribution
function (c.d.f.), its properties and relation with p.m.f and p.d.f. Expectation and theorem of
expectation. Central tendency, Dispersion, Skewness, Kurtosis, Quantiles and Moments
(including absolute and factorial), convex function and moment’s inequalities.
Generating Functions: Probability generating function and moment generating function for
Exponential, Laplace, Logistic, Pareto, Weibul, Log-normal distributions and their properties.
Truncated distributions (discrete and continuous).
Idea, scaling of items according to difficulties, scaling of test scores (Z, Percentile, Thurstone,
equivalent), scaling of rates and ranks, scaling of judgments. Use of continuous distributions in
scaling, income or allied distributions.
References:
1. Chung K.L. (1983): Elementary Probability Theory with Stochastic Process, Springer /
Narosa
2. Feller W. (1968): An Introduction to Probability Theory & its Applications, John Wiley
3. Goon A.M., Gupta M.K. & Dasgupta B. (1994): An Outline of Statistical Theory( Vol-1),
World Press
4. Rohatgi V.K. (1984): An Intro. to Probability Theory & Math. Statistics, John Wiley
5. Hoel P.J., Port S.C. & Stone C.J. ( ): Introduction to Probability Theory (Vol-1), Mifflin &
UBS
6. Cramer H. (1954): The Elements of Probability Theory, John Wiley
7. Parzen E. (1972): Modern Probability Theory and its Applications, John Wiley
8. Uspesky J.V. (1937): Introduction to Mathematical Probability,McGraw Hill
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9. Cacoullos T. (1973): Exercises in Probability. Narosa
10. Rahman N.A. (1983): Practical Exercises in Probability and Statistics, Griffen
11. Pitman J. (1993): Probability, Narosa 12. Stirzaker D. (1994): Elementary Probability, Cambridge University Press 13. Chandra T.K. & Chatterjee D. (2001): A First Course in Probability, Narosa 14. Bhat B.R. (1999): Modern Probability Theory, New Age International 15. Rohatgi VK & Saleh: An Introduction to Probability and statistics 16. Goon AM & Roy D: Problems in probability theory 17. Mukhopadhaya P: Mathematical Statistics
(201-B) Population Statistics (20 marks)
Introduction: Sources of Population Data – Census data, Registration data and the
errors in such data. Rates and ratios of vital events.
Measurements of Mortality: Crude Death rate, Specific Death Rate, Standardized death Rate,
Case fatality rate, Maternal Mortality Rate, Infant Mortality Rate, Neonatal and Perinatal
Mortality Rates.
Life tables: Descriptions of Complete and Abridged Life Tables and their uses, Cohort vs.
Generation Life Tables, Stable population and Stationary population, Construction of complete
life table from population and death statistics.
Measurements of Fertility: Crude Birth Rate, General Fertility Rate, Age Specific Fertility Rate,
Total Fertility Rate.
Measurements of Morbidity: Morbidity incidence and Morbidity prevalence rates.
Measurement of Population Growth: Crude Rate of Natural Increase and Vital Index, Gross and
Net Reproduction Rates.
Population Estimation, Projection and Forecasting: Use of A.P. and G.P. methods for population
estimates. Use of component method for population projection. Derivation of the equation to
the Logistic curve, its properties and fitting to observed data for population forecasting using
Rhode’s, Pear & Reed and Fisher’s method.
References :
1. Goon AM,Gupta MK,Dasgupta B(2001): Fundamentals of Statistics (V-2),World Press
2. Gupta SC & Kapoor VK: Fundamentals of Applied Statistics
3. Spiegelman M. (1980): Introduction to Demography, Harvard University Press
4. Cox P.R. (1976): Demography
5. Biswas S. (1988): Stochastic Processes in Demography and Applications
6. Mishra B.D. (1980): An Introduction to the Study of Population, South Asian Pub.
7. Keyfitz. N and Caswell. H (2005): Applied Mathematical Demography (3rd edition),
Springer
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(202-A) Descriptive Statistics II (25 marks)
Bivariate data – scatter diagram, correlation coefficient and its properties, Coefficient
of determination, Correlation ratio, Correlation Index, Intra-class correlation (equal and
unequal group sizes), Principles of least squares, Concept of Regression, Fitting of polynomial
and exponential curves. Rank correlation (tie and non-tie) – Spearman’s and Kendall’s
measures.
Analysis of Categorical Data: Classification, frequencies and their relation, Consistency of data,
independence and association of attributes, measures of association in 2 x 2, m x n tabels –
Yule’s coefficient, Coefficient of colligation, Pearson’s coefficient, Vandermode’s measures,
Tschuprow’s measures and their inter relationship. Multiple and Partial association.
Goodman-Kruskal’s γ. Odds Ratio. Fitting of logit model through least squares.
References :
1. Goon AM,Gupta MK,Dasgupta B.(1998):Fundamentals of Statistics (V-1),World Press
2. Yule G.U & Kendall M.G(1950): An Introduction to the Theory of Statistics, C.Griffin
3. Kendall M.G. & Stuart A. (1966): Advanced Theory of Statistics (Vols 1 & 2)
5. Croxton F.E., Cowden D.J. & Klein (1969): Applied General Statistics, Prentice Hall
6. Wallis F.E. & Roberts H.V. (1957): Statistics- a new approach, Methuen
7. Lewis-Beck M.S. (edt.) (1993) : Regression Analysis, Sage Publications
8. A.Agresti (1984): Analysis of Ordinal Categorical Data
9. A.Agresti : An introduction to Categorical Data Analysis
10. A.Agresti : Categorical Data Analysis
(202-B) Official & Economic Statistics, Time Series Analysis (25 marks)
Official Statistics
The Statistical system in India: The Central and State Government organizations, the functions
of the Central Statistical Organization (CSO), the National Sample Survey Organization (NSSO)
and WB Bureau of Applied Economics and Statistics.
Source of official statistics in India and WB relating to population, agriculture, industry, trade,
price and employment.
National Income statistics: Income, expenditure and production approaches. Their
applications in various sectors in India.
Economic Statistics
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Index Numbers: Price, Quantity and Value indices, Price Index Numbers: Construction, Uses,
Limitations, Tests for index numbers, various formulae and their comparisons,
Chain Index Number. Some Important Indices: Consumer Price Index, Wholesale Price Index
and Index of Industrial Production – methods of construction and uses.
Measurement of inequality
Gini’s coefficient, Lorenz curves-use of Pareto and Lognormal distributions as income or allied
distributions.
Time series analysis
Introduction: Examples of time series from various fields, Components of a times series,
Additive and Multiplicative models. Trend and Seasonal Components: Estimation of trend by
linear filtering (simple and weighted moving-averages) and curve fitting (polynomial,
exponential, Gompertz and Logistic), Variate Difference method, Detrending. Estimation of
seasonal component by ratio to moving-average method, ratio to trend method, link relatives,
Deseasonalization. Estimation of cyclical variation by Periodogram analysis and Harmonic
analysis.
Stationary Time series: Weak stationarity, Autocorrelation Function, Serial correlation,
Correlogram and lag correlation.
Some Special Processes: Moving-average (MA) process and Autoregressive (AR) process of
orders one and two, Estimation of the parameters of AR(1) and AR(2) – Yule-Walker
equations.
Exponential smoothing method of forecasting.
References:
1. C.S.O. (1984) : Statistical System in India
2. Goon A. M.,Gupta M. K,, and Dasgupta. B. (2001): Fundamentals of Statistics (V-2),World
Press
3. Yule G.U. & Kendall M.G. (1953): An Introduction to the Theory of Statistics, C.Griffin
4. Kendall M.G. & Stuart A. (1966): Advanced Theory of Statistics (Vol 3), C.Griffin
5. Croxton F.E., Cowden D.J. & Klein (1969): Applied General Statistics, Prentice Hall
6. Mudgett B.D. (1951): Index Numbers, John Wiley
7. Allen R.G.D. (1975): Index Numbers in Theory and Practice, Macmillan
8. Mukhopadhyay P. (1999): Applied Statistics
9. Johnston J. & Dinardo J. (1997): Econometric Methods, McGraw Hill
10. Nagar A.L. & Das R.K. (1976): Basic Statistics
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11. Kendall M.G. (1976): Time Series, Charles Griffin
12. Chatfield C. (1980): The Analysis of Time Series –An Introduction, Chapman & Hall
13. Mukhopadhyay P. (1999): Applied Statistics
14. Johnston J. & Dinardo J. (1997): Econometric Methods, McGraw Hill
15. MOSPI website
16. DOSPI, WB website
17. Gupta SC & Kapoor VK: Fundamentals of applied statistics
203 PRACTICAL (50 marks)
Practical problem based on paper 201-A (Probability Theory II i.e., fitting of probability
distribution and scaling), 201-B (Population Statistics), 202-A (Descriptive Statistics-II) and
202-B (Economic Statistics, Time Series Analysis).
Semester – III
(301-A) Linear Algebra (30 marks)
Vector Algebra: Introduction, addition and scalar multiplication. Linear combination,
linear dependence and independence. Vector spaces with real field and vector subspaces,
Concept of Spanning, Basis and dimension of a vector space, Euclidean Space: inner product
and Orthogonality, Gram-Schmidt Orthogonalization, Orthogonal basis, Ortho-complement of
Subspace.
Matrix Algebra: Matrices, Matrix operations, Different types of matrices (including non-
singular and orthogonal) and elementary transformations. Partition of a matrices.
Determinants: Definition, Properties, Evaluation of some standard determinants.
Inverse matrix: Definition & Properties .Inverse of some standard matrices.
Rank of a matrix: Row space and column space, concept of rank, standard results on rank.
Methods of finding rank: Echelon Matrices, the sweep-out and the pivotal condensations,
normal form, minor and rank. Null space and rank. Rank factorization.
Linear Transformation: Kernel & Image, Matrix representation.
System of linear equations: Homogeneous and non-homogeneous systems – conditions for
solvability. Gaussian Elimination.
Quadratic forms; classification and canonical reduction. Properties of n.n.d /n.p.d matrices.
Characteristic roots and vectors of a matrix, Properties of Characteristic roots and vectors of
symmetric matrix and canonical reduction of quadratic forms. Cayley -Hamilton theorem.
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References:
1. Hadley G. (1995): Linear Algebra, Addison Wesley/ Narosa
2. Rao A.R. & Bhimasankaran P. (1996): Linear Algebra
3. Searle S.R. (1982): Matrix Algebra – useful for Statistics, John Wiley
4. Rao C.R. (1974): Linear Statistical Inference & its Applications, Wiley Eastern
5. Rao C.R. (1952) : Advanced Statistical Inference in Biometric Research, John Wiley
6. Goon AM: Vectors and Matrices
7. Mapa SK: Abstract and linear algebra
(301-B) Probability Theory III (20 marks)
The p.m.f., p.d.f. and c.d.f. in bivariate case. Marginal and Conditional distributions,
Independence, Conditional Expectation and variences, Correlation and Regression. Theorems
on sum and product of expectations of random variables, generating functions in bivariate
cases.
Compound distribution (binomial and poisson).
Probability Inequalities: Markov’s inequality, Chebychev’s lemma & Chebychev’s inequalities
(one and two sided). Convergence in probability, Convergence in Distribution and related
results. Weak law of large numbers and its applications. Central limit theorem (IID case only),
De Movire-Laplace, Liapounoff’s and Lindeberg-Levy limit theorem as an application of CLT.
Bivariate Normal Distribution and its properties.
References:
1. Chung K.L. (1983): Elementary Probability Theory with Stochastic Process, Springer /
Narosa
2. Feller W. (1968): An Introduction to Probability Theory & its Applications, John Wiley
3. Goon A.M., Gupta M.K. & Dasgupta B. (1994): An Outline of Statistical Theory (Vol-1),
World Press
4. Rohatgi V.K. (1984): An Intro. to Probability Theory & Math. Statistics, John Wiley
5. Hoel P.J., Port S.C. & Stone C.J. ( ): Introduction to Probability Theory (Vol-1), Mifflin &
UBS
6. Cramer H. (1954): The Elements of Probability Theory, John Wiley
7. Parzen E. (1972): Modern Probability Theory and its Applications, John Wiley
8. Uspesky J.V. (1937): Introduction to Mathematical Probability,McGraw Hill
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9. Cacoullos T. (1973): Exercises in Probability. Narosa
10. Rahman N.A. (1983): Practical Exercises in Probability and Statistics, Griffen
11. Pitman J. (1993): Probability, Narosa
12. Stirzaker D. (1994): Elementary Probability, Cambridge University Press
13. Chandra T.K. & Chatterjee D. (2001): A First Course in Probability, Narosa
14. Bhat B.R. (1999): Modern Probability Theory, New Age International
15. Rohatgi VK & Saleh: An Introduction to Probability and statistics 16. Goon AM & Roy D: Problems in probability theory 17. Mukhopadhaya P: Mathematical Statistics
(302-A) Statistical computing in C (25 marks)
Introduction to computers: Positional number system. Binary arithmetic, Binary, Octal and Hexadecimal representation of integer and real numbers. Computer memory, Operating system, Computer languages, Problem solving using computer. Introduction to C, Historical development, The C character set - constants, variables and keywords. Types of C constants and variables. C instruction-Type Declaration Instruction; Arithmetic Instruction, Integer and Float conversion, Type conversion in Assignment. Control instructions. The Decision Control Structure-if statement; Multiple Statements within if, if-else statement; Nested if else; Forms of if. Use of Logical operators. The Loop Control Structure-while loop, for loop; Odd loop; Break Statement; Continue Statement; do-while loop. Case control Structure-Decisions using switch; go to statement. Function - use of functions; Pointers. Floats and doubles. Storage classes in C. C Pre-processor - features-; - Arrays-Pointers and Arrays. Structures; Array of Structure. Input / Output in C- Types of I/O; Console Input/ Output functions. Disk I/O functions. I/O Redirection in DOS.
References: 1. Kanetkar Y: Let Us C
2. Chatterjee AX & Chatterjee T: Computer applications of mathematics and statistics
3. Xavier C: C language and numerical methods
4. Rajaraman V: Fundamentals of computers
5. Sarma K.V.S.: Statistics Made Simple-Do it yourself on PC
(302-B) Multivariate Analysis (25 marks)
Multivariate data – multiple regressions and partial regression coefficients, multiple
correlation and partial correlation – their properties and related results.
Random Vector: Probability mass and density functions, Distribution Function, Mean vector
and Dispersion matrix, Marginal and Conditional Distributions, Ellipsoid of Concentration,
Multiple Regression, Multiple Correlation, Partial Correlation in the cocept of probability
distribution.
Multivariate Distributions: Multinomial, Multivariate Normal distributions and their
properties.
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References:
1. Kendall M.G. & Stuart A. (1966): Advanced Theory of Statistics (Vol 3), C.Griffin
2. Anderson T.W. (1958): An Introduction to Multivariate Statistical Analysis, 3rd edition,
Wiley interscience
3. Goon A.M., Gupta M.K. & Dasgupta B. (1994): An Outline of Statistical Theory (Volumes
1 & 2), World Press
4. Rohatgi V.K. (1984): An Introduction to Probability Theory & Math. Statistics, John
Wiley
5. 0Johnson, N.L. & Kotz S. (1970): Distributions in Statistics, John Wiley
7. Rao C.R. (1974): Linear Statistical Inference and its Applications, John Wiley
8. Mukhopadhyay P. (1996): Mathematical Statistics
9. Johnson R. A. and Wichern, W (2001): Applied Multivariate Statistical Analysis, 5th
edition, Prentice Hall
(303-A) PRACTICAL based on paper 302-A (25 marks)
Programs: 1. Computing AM, GM, and HM of grouped and ungrouped data. 2. Sorting data set; finding minimum and maximum. 3. Computing median, the first and second quartiles. 4. Computing range, variance and quartile deviation. 5. Computing moments and quantiles of ungrouped and grouped data 6. Factorial of a positive integer. 7. Correlation Coefficient of ungrouped and grouped data. 8. Fitting a straight line or an exponential curve to a given data. 9. Fitting Binomial and Poisson distributions. 10. Transpose, addition and multiplication of matrices; finding inverses and determinants of square (non-singular) matrices. 11. The Sweep-out and Pivotal Condensation methods. 12. Solutions of equations (Iteration, N-R, Bisection methods) 13. Interpolation by Lagrange’s formula 14. Numerical Integration (Simpson’s ⅓rd, Trapezoidal) 15. Generation of random sample from normal distribution
(303-B) PRACTICAL (25 marks)
Practical problem based on paper 301-A (Linear Algebra), 302-B (Multivariate Analysis).
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Semester-IV
(401-A) Sampling Distributions & Statistical Inference I (35 marks)
Sampling Distributions
Transformation of Random variables (one and more than one).
Introduction: Concepts of Random Sampling, Statistics and Sampling Distributions of Statistics
and its standard error. Illustrations using different distributions, reproductive properties of
the distributions.
Some Standard Sampling Distributions: Distributions of the mean and variance of a random
sample from a normal population. , t and F distributions-derivation and properties.
Distributions of means, variances and correlation coefficient (null case) of a random sample
from a bivariate normal population, distribution of the simple regression coefficient (for both
stochastic and non-stochastic independent variable cases).
Distributions of Order Statistics and Sample Range.
References:
1. Goon A.M., Gupta M.K. & Dasgupta B. (1994): An Outline of Statistical Theory (Vol-1),
World Press
2. Johnson, N.I. & Kotz S. (1970): Distributions in Statistics, John Wiley
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3. Ross S.M. (1972): Introduction to Probability Models, Academic Press
4. Mood A.M., Graybill F. & Boes D.C. (1974): An Introduction to the Theory of Statistics
(3rd ed), McGraw Hill
5. Rao C.R. (1952): Advanced Statistical Methods in Biometric Research, John Wiley