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Syllabus For B.A./ B.Sc. I, II, III W.E.F. 2017

For B.A./ B.Sc. Part I and Part II , in Statistics , there will be THREE theory papers and ONE practical paper of three hours duration each. Each theory paper as well as practical paper will carry 50 marks . For practical , there shall be 08 and 06 marks for practical records and viva voce respectively .

For B.A./ B.Sc. Part III , in Statistics , there will be FOUR theory papers paper of three hours duration each and ONE practical paper of four hours duration . Each theory paper will carry 55 marks and practical paper will carry 80 marks. For practical, there shall be 12 and 08 marks for practical records and viva voce respectively.

SCHEDULE OF PAPERS

B.A./ B.Sc. I

Paper I : Probability Theory

Paper II : Descriptive Statistics

Paper III : Numerical Methods and Applied Statistics

PRACTICAL Problems based on paper II & III

B.A./ B.Sc. II

Paper I : Theory of estimation and design of experiments

Paper II : Testing of Hypothesis and Sampling Distribution

Paper III : Sampling Techniques

PRACTICAL Problems based on paper I, II & III

B.A./ B.Sc. III

Paper I : Theory of Matrices and Statistical Quality Control

Paper II : Numerical Methods

Paper III : Distribution Theory

Paper IV : Statistical Inference

PRACTICAL Problems based on paper I & II

B.A. / B.Sc. Part - I

STATISTICS Paper - I Probability Theory Maximum Marks-50 Duration-3 hrs.

UNIT – I Random Experiment, Sample space and event, Exhaustive, Mutually exclusive and equally likely events, Mathematical, Statistical and Axiomatic definition of Probability, Probability of sure and impossible events, Probability of union and intersection of events, Subadditivity (Boole’s inequality), Conditional Probability, Multiplication law of Probability, Marginal Probability, Independent events, pairwise Independent and Mutually Independent events.

UNIT – II Random variable, Descrete, and continuous random variables, Independent random Variables. Univariate distribution, Probability mass and density function, distribution function and its properties. Bivariate distribution, Joint probability density function, Joint probability mass function, Marginal and conditional distribution of random variables, Examples.

UNIT – III Mathematical expectation: Theorems on the expectation including sum of random variables and product of independent random variables. Co-variance and independence of variables. Expectation and variance of a linear combination of random variables. Conditional expectation and conditional variance. Moment and moment generating function, Limitation of moment generating function, Theorem on moment generating function, Cumulantes, Additive property of cumulantes.

UNIT – IV Study of some Standard Distributions: Bernoulli, Binomial, Poisson and Normal distribution, Mean, Variance, Moments, M.G.F. and recurrence relations of these distributions, Poisson distribution as limiting form of binomial distribution, Normal distribution as limiting form of Binomial and Poisson distribution, Important Properties of the distributions.

UNIT – V Law of total probability, Bayes’ theorem , Examples , Repeated trials, Chebyshev’s inequality, Examples Elementary ideas of convergence in probability, Theorem of Bernoulli and Tshebycheff ’s week law of large number, Central limit theorem (without proof) for independently and identically distributed random variables and its appIication. Importance of the normal distribution in Statistics. Cauchy- Schwartz and Jansen’s inequality (without proof), Examples.

P.T.O.

Books Recommended

1. Goon, Gupta & Dasgupta Fundamental of Statistics Vol. I

2. Gupta and Kapoor Fundamental of Mathematical Statistics

3. Kapoor and Saxena Mathematical Statistics

4. Umarji, R.R. Probability and Statistical Method

5. Hoel, P.G. Introduction to Mathematical Statistics

6. Mukharji, K.K. Probability and Statistics

7. Hogg and Craig Introduction to Mathematical Statistics

8. Paul Mayer Probability Theory

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There shall be three papers of three hours duration each carrying 50 marks. Each theory paper is divided into five units. There shall be 6 questions in all in each theory paper consisting of 2 questions from each unit and a compulsory question consisting of 10 short answer type questions based on the contents of all the five units. Examinees will be required to answer 6 questions in all selecting one question from each unit and a compulsory question.

B.A./B.Sc. Part –I

STATISTICS

PAPER –II

Descriptive Statistics

Maximum Marks -50 Duration – 3hrs.

Unit – 1

Types, Collection and Representation of Data

Attribute and variables, Discrete and continuous data ,Frequency and non frequency data, primary data, secondary data, frequency distribution, Graphical representation of group of frequency distribution, Histogram, Frequency polygon, frequency curve. Cumulative frequency curve, relative frequency.

Analysis of quantitative data:

Measure of location mean,(AM,GM, HM), properties of the AM, Weighted mean, Median, Median by graph, Mode, Mode by graph, Derivation of Mode formula, Application of mean, Median and Mode. Merits and demerits of AM, GM, HM, Median and Mode.

Unit – II

Partition values (Quartile, Deciles, Percentiles), Measure of dispersion, Range, Quartile deviation, Mean Deviation about (mean, median, mode), minimal properties of median. Mean square deviation, Root mean square deviation, Variance and S.D., relation between root mean square deviation and S.D., Effect of change of origin and scale on variance, Relation between S.D. and M.D. about mean, mean and S.D. of a composite set, Coefficient of dispersion, Coefficient of variation and its application, Application of range, M.D. and S.D. .

Unit – III

Moment: Central moment and moment about arbitrary origin, Relation between central moments and arbitrary moments and vice – versa, Sheppard’s correction (without proof) for moments up to fourth order. Effect of change of origin and scale on moments, Charlie’s checks, Factorial moments, Absolute moments, Relation between ordinary and simple factorial moments, Pearson’s β and γ – coefficients.

Skewness and Kurtosis : Symmetrical frequency distribution of discrete as well as continuous variable and its curve, properties of symmetrical distribution, Skewness, Measure of skewness, positive and negative skewness, Kurtosis, Measure of kurtosis (Mesokurtic, Platykurtic, Leptokurtic).

P.T.O.

Unit – IV

Bivariate Data: Scatter diagram, Bivariate frequency distribution, Karl Pearson’s correlation coefficient and its underlying assumption, Limit of correlation coefficient, repeated ranks, Condition for maximum and minimum rank correlation coefficient, effect of change of origin and scale on correlation coefficient, Rank correlation coefficient, repeated ranks, Condition for minimum and maximum rank correlation coefficient, regression curve, Line of regression, regression coefficient and its properties, Angle between two line of regression, Reason for two line of regression, residual variance.

Unit - V

Method of least square and fitting of different type of curve (algebraic, polynomial, power, exponential, and hyperbolic functions), Most plausible solution of system of linear equations, The line of closest fit.

Intra class correlation and its limit, correlation ratio.

Multivariate data

Linear regression involving three variables, Properties of residuals, variance of residuals, Muiltiple and partial correlation coefficient and their properties.

Books Recommended

1. Goon, Gupta & Dasgupta Fundamental of Statistics Vol. I 2. Gupta and Kapoor Fundamental of Mathematical Statistics 3. Kapoor and Saxena Mathematical Statistics 4. Yule & Kendal An Introduction to theory of Statistics 5. Kenney and Keeping Mathematics of Statistics 6. Weather Burn A first course in Mathematical Statistics 7. Gupta, C.B. An introduction to Statistical method 8. Sharma & Goyal Mathematical Statistic

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There shall be three papers of three hours duration each carrying fifty marks. Each theory paper is divided into five units. There shall be 6 questions in each theory paper consisting of 2 questions from each unit and a compulsory questions consisting of 10 short answer type questions based on the contents of all five units. Examinees will be required to answer 6 questions in all selecting one question from each unit and a compulsory question.

B.A. /B.Sc. Part –I STATISTICS

Paper –III

Numerical Methods and Applied Statistics

Maximum Marks -50 Duration -3 hrs.

Unit –I

Finite difference theory, basic property, Forward and backward difference operators, Difference tables (Forward and backward), Displacement operator (Shift operator), properties of operator  and E, nth difference of pn(x). Difference of some special functions such as trigonometrical, Exponential, Logarithmic, Relations between E and  and E and  , method of separation of symbols, Factorial polynomial, Difference of a factorial polynomial.

Unit –II

Representation of Pn(x) in the form of factorial polynomial, Detached coefficients method (Synthetic Divison Method), Interpolation with equal interval, interpolation meaning, assumptions and accuracy, method of interpolation, Newton’s GregoryForward and Backward interpolation formulae for equal intervals, Newton's advancing difference formula, Application of Newton’s formulae, Estimate of missing value of f(x) with the help of known values. Binomial expansion method (only one or two missing values).

Unit –III

Interpolation with unequal intervals: Divided differences with divided difference tables, properties of divided differences, Newton’s Divided difference formula, Relation between divided and ordinary differences, Lagrange’s Interpolation formula, Central difference formula due to Gauss’s ( Forward and Backward) Sterling’s formula, Bessel’s formula and Laplace – Everatt formula, Sheppard’s central difference operators,  ,μ,, ,, E,D, and their relations.

Unit – IV

Index number: Definition, Price relatives and quantities or volume relatives, Link and chain, relatives, Price and quantity index numbers, their uses and relative merits, Computation of index numbers, Laspeyre’s, Pasche’s, Marshal-Edworth’s and Fisher’s Index number, chain base index number, cost of living index no. (consumer price index number), Time and factor reversal tests, circular test, construction of cost of living index number, Limitations of index numbers.

Economic statistics Time series analysis: Economic time series , different components of a time series , illustrations, additive and multiple models, determination and trends by free hand drawing, Semi-average method, moving average ( only first degree curve) and fitting of mathematical curves, construction of

P.T.O.

seasonal indices by method of monthly averages , Ratio and trend, Ratio to moving average and link relative method.

Unit –V

Demographic Methods

Sources of demographic data: Census, registration, ad-hoc surveys, hospital records, measurement of mortality and life table; cause death rate, age specific death rate, Standardized death rate, infant mortality rate complete life table, and its main features, uses of life table, stationary and stable population, measurement of fertility : crude birth rate, general fertility rate, age-specific fertility rate, total fertility rate, sex ratio, Gross reproduction rate , net reproduction rate .

Theory of attributes

Dichotomy, classes and class frequencies, order of classes, relation between class frequencies, Ultimate classes and ultimate class frequency, Consistency of data, independence of attributes, Association of attributes, Yule’s coefficient of association, Contingency table.

Books Recommended:

1. H. C. Saxena Finite differences and Numerical analysis 2. Kapoor & Saxena Numerical Analysis 3. Goon, Gupta & Dasgupta Applied Statistics 4. Gupta & Kapoor Fundamental of Mathematical Statistics 5. Freeman, H. Finite differences for Actuarial students

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B.A. /B.Sc. Part –II

STATISTICS

Paper –I

Theory of estimation and design of experiments

Maximum Marks -50 Duration -3 hrs.

Unit –I

Theory of point estimation: Introduction of estimation, Definition of estimator (Statistic) and estimate, Properties of estimators: Unbiasedness, Biased estimator, Under and over estimate, Best unbiased linear combination of two unbiased estimator of a parameter. Consistency: Unbiased consistent and biased consistent estimator of population variance, Sufficient conditions for consistency. Efficiency : Efficient estimator and efficiency of the estimator, Cramer Rao Inequality, condition for equality in the Cramer Rao inequality, Regularity condition.

Unit –II

Minimum variance unbiased estimator, MVUE is unique, Correlation between MVUE and unbiased estimator, Linear combination of MVUE and unbiased estimator.

Sufficiency: Concept of sufficient estimator, Rao -Black theorem, Fisher –Neyman Factorization theorem (statement only).

Definition of complete and exponential family of probability densities.

Unit –III

Method of estimation: Definition of likelihood function, Difference between likelihood function and joint probability function, Likelihood estimator, Properties of Maximum likelihood estimator (without proof), Minimum Chi- square and modified minimum Chi- square method, Method of moment, Criterion for MLE and moment estimators are identical, Method of least square.

Unit- IV

Analysis of Variance: analysis of variance (under fixed effect model) in one way, two way and three way classification with equal number of observations per cell (one as well as more than one).

Unit -V

Design of experiment: Basic principles of design, Randomization, replication and local control, Completely Randomized Design, Randomized Block design and Latin square Design.

P.T.O.

Books Recommended

1. S.C. Saxena Statistical Inference

2. Hogg and Craig Introduction to Mathematical Statistics

3. Mood and Graybill Introduction to the theory of Statistics

4. Kandal and Silvery Advance theory of Statistics Vol. II

5. S.D. Silvery Statistical Inference

6. Goon, Gupta & Dasgupta Fundamental of Statistics Vol. II

7. Gupta and Kapoor Applied Statistics

8. Goon, Gupta & Dasgupta An Outline of Statistics Vol. II

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B.A. /B.Sc. Part –II

STATISTICS

Paper –II

Testing of Hypothesis and Sampling Distribution

Maximum Marks -50 Duration -3 hrs.

Unit –I

One to one transformation of random variable of discrete and continuous type in one and two random variables.

Unit –II

Order statistic and its application, Sampling distribution of order statistics, p.d.f. of asingle order statistic and ith order statistic, Joint p.d.f. of two order statistic, Distribution of the range and the median, Sampling distribution of a statistic, Standard error., Standard error of the mean and variance, utility of standard error.

Unit –III

Beta (1st kind and 2nd kind ) distribution, Gamma Distribution, Derivation of Chi –Square, Student-t and Snedecors –F distribution, Constants of above distribution, Additive property of Gamma and Chi-square distribution, Ratio of two Independent Gamma and Chi-square variate, Limiting form of t, chi-square and gamma distribution.

Unit –IV

Statistical hypothesis, Simple and composite hypothesis, testing of a statistical hypothesis, Null and alternative hypothesis, Critical region, Best critical region, Two types of error, Level of significance, Power of C.R. (or a test), Concept of most powerful and uniformly most powerful test, one tail and two tailed test, critical values(or significant values), test statistic, procedure for testing of hypothesis, testing a simple hypothesis against a simple alternative.

Unit –V

Application of t , F, and Chi-square distribution, test of significance-Large sample test, small sample test based on t, F and Chi square distribution, Fisher’s transformation and its applications, Contingency table, Yate’s correction, Inter relation between t, F, Chi –square distribution.

P.T.O.

Books Recommended

1. Hogg and Craig Introduction to Mathematical Statistics

2. Kendal and Stuart Advance theory of Statistics Vol. I & II

3. Lehmann Testing Statistical Hypothesis

4. Goon, Gupta & Dasgupta An outline of Statistics Vol. I

5. Gupta and Kapoor Fundamental of Mathematical Statistics

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B.A. / B.Sc. Part -II

STATISTICS Paper - III Sampling Techniques Maximum Morks-50 Duration-3 hrs.

UNIT – I Complete enumeration vs sampling, Requirements of a good sample, The principal steps in sample survey, Random and non- random method of sampling, Concept of sampling and non-sampling errors, Concept of the estimate, Sampling variance, Standard error and mean square error.

UNIT – II Simple Random Sampling: Procedure of selecting a random sample (WR and WOR) , Use of random number table. Estimate of population mean and population total, sampling variance and S.E. of the estimates, Estimate of sampling variance SRSWR and SRSWOR, Comparison between SRSWR and SRSWOR .

Sampling for Proportions: Estimate of Population proportions SRSWR and SRSWOR, sampling variance of the estimates, Estimate of sampling variance in SRSWR and SRSWOR.

UNIT – III Stratified Random Sampling: Definition and procedure of stratified random sampling, Sample mean and unbiased Estimate of population mean and variance of the unbiased estimate, Estimate of sampling variance, Allocation of sample size in different strata, Variance of the unbiased estimate under different system of allocation (Proportional, optimum and Neyman),Comparison of the stratified random sampling (under proportional and Neyman allocation) with simple random sampling, Gain due to stratification.

UNIT – IV Ratio Method of Estimation: Procedure, Usage and importance of ratio method of estimation ,Ratio estimate of population mean, The limit of the bias of ratio estimate, First approximation of the Expectation , bias and variance of the ratio estimate(up to first approximation), Condition under which ratio estimate is unbiased, Optimum property of ratio estimate, Efficiency of the ratio estimate over SRS. Estimate of the variance of the ratio estimate.

Systematic Sampling: Procedure, schematic diagram and usage of systematic sampling, Estimate of the population mean and variance of the estimate (N=nk and N is not equal to nk). Comparison of systematic sample with the simple random sample and stratified random sample in terms of usual intra-class correlation coefficient, the comparison for the population with linear trend among SRS, stratified, systematic sampling.

Circular Systematic Sampling: Procedure, estimate of population mean , variance of the estimate.

P.T.O.

UNIT – V Cluster Sampling (Equal Cluster Size): Procedure and importance, Estimate of the population mean and the sampling variance, sampling variance in terms of intra-class correlation coefficient, Estimate of sampling variance. Relative efficiency of cluster sampling w.r.t. simple random sampling in terms of intra-class correlation coefficient.

Two Stage Sampling (Equal f.s.u.) : Procedure and usage, Estimate of population mean and variance of the estimate, Estimate of the variance of sample mean, Allocation of sample size to the two stages (Equal and unequal per unit cost in both stages), Comparison of the two stage sample with the one stage in terms of intra-class correlation coefficient.

Books Recommended:

1. Sukhatme and Sukhatme Sampling Theory of Surveys with Application 2. Cochran Sampling Techniques 3. Des Raj Sampling theory 4. Singh and Chaudhary Theory and Analysis of Sample Survey Designs

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B.A. /B.Sc. Part –III

STATISTICS

Paper –I

Theory of Matrices and Statistical Quality Control

Maximum Marks -55 Duration -3 hrs.

Unit –I

Adjoint and Inverse : Partitioned matrices ,Trace of matrix, properties of trace, Idempotent matrices, nilpotent matrix, triangular matrices and its product, Generalized inverse of matrix and its properties, Matrix polynomials, rank of matrix, theorems on rank , elementary transformations, elementary matrices, reduction to normal form of matrix .

Unit – II

Vector and vector spaces, Linear dependence of vectors, Sub – space, Basis and dimension of a sub – space, rank of sum of two matrix, rank of symmetric matrix, Solution of linear equations, Frobeneous theorem, latent roots and latent vectors, Cayley Hamilton theorem.

Unit – III

Bilinear form and quadratic form, Discriminent of Q.F., Linear transformation, Congruence of Q.F. and matrices, Elementary congruent transformations, Q.F. in real field, Reduction to canonical form, Rank , Index and signature of Q.F., necessary & sufficient conditions for a positive definite Q.F., Quadratic characteristics properties of definite, Semi definite form and indefinite Q.F., Gram matrix , Cochran theorem.

Unit – IV

Inner product of two vectors, orthogonal vectors, Normal vectors, orthogonal matrices and its properties, Determination of a real orthogonal matrix, N and S condition for a square matrix to be orthogonal, orthogonal transformations, Modulus of an Orthogonal transformation, orthogonal reduction of a real symmetric matrix.

Unit – V Statistical quality control, chance and assignable causes of variation , uses of SQC, control charts, 3 control limits, X and R charts,  charts, Control chart for fraction defective, Control chart for number of defective and control chart for number of defects, Natural tolerance limits and specification limits, Acceptance sampling by attributes, acceptance quality level, Lot tolerance proportion defective (L.T.P.D.), Process average fraction defective, Consumer’s risk , Producer’s risk, Average out going quality limits, O.C . curve, average sample number, Single sampling plan, double sampling plan.

P.T.O.

Books Recommended

1. Shanti Narain Text Book of Matrices 2. Kapoor and Singhal Matrices 3. Goyal and Sharma Linear Algebra 4. D. T. Finkbeiner Introduction to Matrices and & Linear transformation 5. Gupta & Kapoor Applied Statistics 6. Goon, Gupta & Das Gupta Fundamentals of Applied Statistics Vol. II

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There shall be four papers of three hours duration each carrying 55 marks. Each theory paper is divided into five units. There shall be 6 questions in all in each theory paper consisting of 2 questions from each unit and a compulsory question consisting of 10 short answer type questions based on the contents of all the five units. Examinees will be required to answer 6 questions in all selecting one question from each unit and a compulsory question.

B.A. / B.Sc. Part –III

STATISTICS

Paper – II

Numerical Methods

Maximum Marks - 55 Duration – 3hrs.

Unit – I

Remainder Terms in Newton’s, Lagrange’s, Sterling’s and Basel’s formula, Difference of zero, Curve fitting by Orthogonal Polynomials, Inverse interpolation (only proof).

Unit –II

Numerical Differentiation: Summation of series, relation between  and  , Summation by parts, Application of the relation between  and  .

Unit –III

Numerical Integration: General quadrature formula,Trapezoidal Rule, Simpson’s One third and Three eight rule , Gauss quadrature formula, Weddle’s rule, Central difference – quadrature formulae, Central – difference quadrature formulae, Lobatto’s formula, Euler Maclaurin’s summation formula and its application.

Unit –IV

Difference equation : Definition, Properties of difference equations, Order of difference equations, Solution of a difference equation (general solution and particular solution). Linear homogeneous and non-homogeneous difference equation of the Ist order with constant coefficient and with variable coefficients. Application of difference equations.

Unit –V

Solution of algebraic and Transcendental equations: Synthetic division method, Graphical method , Regula Falsi method( Method of false position) , Newton’s – Raphson method ,Iterative method and Graeffe’s Root squaring process, Solution of ordinary differential equations( First order): Eular’s Method, Euler’s modified method, Runge Kutta method, Picards method, Milne’s method.

P.T.O. Books Recommended

1. Scarborough Numerical Mathematical Analysis 2. Liebartain A course in Numerical Analysis 3. Freman Finite Differences for Actuarial students 4. H.C. Saxena Finite Difference and Numerical Analysis

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B.A. /B.Sc. Part –III

STATISTICS

Paper –III

Distribution Theory

Maximum Marks -55 Duration -3 hrs.

Unit –I

Generating function , Probability Generating function of a random variable, Mean and Variance in terms of P.G.F, Moment generating function in terms of P.G.F., Mean and Variance of Binomial, Poisson and Geometric distribution using P.G.F. , Probability generating function of linear function of random variables, Sum of a fixed number of random variables, Sum of a random number of discrete random variables , convolution of sequences .

Unit –II

Laplace transformation and its properties (with proof), Laplace transform of a probability distribution ( or of a random variable), Laplace transformation of the distribution function , Mean and Variance in terms of L.T., Mean and Variance of Poisson, Exponential, Gamma and Uniform distribution , Some theorems based on L.T. of probability distribution , L.T. of the sum of two & more random variables , L.T. of sum of a random number of continuous random variables .

Unit –III

Compound random variable, Compound distribution, Compound Binomial and Poisson distribution. Pearsonian distribution , determination of the constants of Pearsonian differential equation , Mean and Mode of the distribution , General solution of Pearsonian differential equation , Criterion ‘K’ , Pearsonian type –I, II, III,IV, V, VI, VII and Normal curve.

Unit –IV

Discrete distribution: Uniform distribution : mean, variance and m.g.f. , Hypergeometric distribution: mean, Variance and study of its limiting case, Multinomial distribution: m.g.f., mean, variance and covariance, Negative binomial distribution : m.g.f., mean , variance, cumulants and limiting case, Geometric distribution : mean , variance and lack of memory property, Power Series distribution an its properties.

Unit –V Continuous distribution: Non-Central chi square distribution : Additive properties, cumulants, Non-Central t- distribution and its p.d.f., Non-Central F- distribution and their properties, Exponential distribution : mean ,variance , m.g.f., lack of memory property, cumulants and its application, Log Normal distribution : Moments, mean, variance, median, mode, properties and its application, Uniform distribution : Moments, m.g.f., M.D. and its important application, Pareto distribution : moments and its application ,Weibull distribution : moments and its application .

P.T.O. Books Recommended

1. Goon, Gupta and Das Gupta An Outline of Statistical theory Vol. I

2. Hogg and Craig Probability Statistical Inference

3. Johnson and Kotz Distribution in Statistics Vol. I, II, & III

4. Medhi, J. Stochastic Process

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B.A. /B.Sc. Part –III

STATISTICS

Paper –IV

Statistical Inference

Maximum Marks -55 Duration -3 hrs.

Unit –I

Definition of Sufficiency, Fisher Neymann Factorization theorem for discrete and continuous cases, Minimal sufficient Statistics, Complete family of distribution, Boundedly complete, Complete sufficient statistic, Uses of complete sufficient statistic, Most general form distribution possessing sufficient estimators.

Unit –II

Bhattacharya’s Bound, Lehman Scheffe’s theorem, BAN estimator, properties of Maximum likelihood estimator, Successive approximation to ML estimators.

Unit –III

Interval estimation: Definition of interval estimation, Confidence interval and confidence coefficient, Simple method of obtaining confidence limits, Confidence Belt, a most general method of obtaining confidence limits, Shortest confidence intervals, Shortest unbiased confidence interval. Theory of confidence set, Correspondence between testing of hypothesis and confidence intervals.

Unit –IV

Non-Parametric Tests: Concept of Distribution free tests. Consistency and relative efficiency of test, Treatment of ties and randomized test, Chi square test as goodness of fit, Kolmogorov-Smirnov one sample and two samples test, Comparison of the Chi square and KS tests. The ordinary sign test, paired sample sign test, Wilcoxon signed –rank test, Wilcoxon paired sample signed rank test, Rank test, Median test.

Unit –V

Testing of hypothesis, Randomized and non-randomized test, Construction of MP and UMP critical region, MP and UMP regions in random sampling from normal population, Optimum regions and sufficient region.

P.T.O.

Books Recommended

1. T.S. Forgusen Mathematical Statistics Decision Theory

2. E. L. Lehmann Notes on theory of Estimation

3. E. L. Lehmann Testing of statistical hypothesis

4. B.W. Silvey Statistical Inference

5. V. K. Rohatagi An Introduction t o Probability & Mathematical Statistics

6. Gibbons Non Parametric Statistical Inference

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