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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 ******** 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 ********************* 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