ba/bsc course in statistics - kumaun universitykunainital.ac.in/forms/static/syallabus for ba...

BA/BSc COURSE IN STATISTICS

TO BE IMPLEMENTED FROM SESSION 2016-17 ONWARDS

(THERE WILL BE A TOTAL OF SIX SEMESTERS OF 150 MARKS, INCLUDING TWO

THEORY PAPERS OF 50 MARKS EACH AND A PRACTICAL CARRYING 50

MARKS IN EACH SEMESTER)

SEMESTERWISE DISTRIBUTION OF PAPERS WITH MARKS

SEMESTER I

Random experiments, events, algebra of events, definition of probability of an

event: classical, statistical and axiomatic approach . Conditional probability ,

theorem of compound probability, Bayes’ theorem ,independence of events.

Random variables: discrete and continuous, distribution functions - probability

mass function and probability density function. Joint distribution of two

random variables, marginal and conditional distribution, independence of two

random variables, Expectation, theorem on expectation of sum of random

variables and product of independent random variables, conditional

expectation . Moments and Moment Generating function, Chebychev’s

inequality, weak law of large numbers and Central Limit Theorem (without

proof).

PAPER II: STATISTICAL METHODS

MAX MARKS:50

Statistical data, frequency table, graphical representation, Measures of

Location and measures of dispersion, Moments, Factorial moments, Skewness

and Kurtosis, Association of attributes and contingency tables. Method of least

squares and curve fitting . Bi-variate data-regression and multiple correlation,

correlation ratio, Tri-variate data- partial and multiple correlation

PAPER III: PRACTICAL BASED ON PAPER I & II

SEMESTER II

PAPER I: THEORETICAL DISTRIBUTIONS: DISCRETE AND CONTINUOUS

DISCRETE: Binomial, Poisson, Geometric, Hyper Geometric, Negative-Binomial, Rectangular CONTINUOUS: Uniform, Normal, Log Normal, Exponential, Gamma and Beta distributions with properties and goodness of fit Bi-variate normal distribution and its properties. PAPER II: APPLIED STATISTICS

Index Number and their uses, tests for index numbers, cost of living index numbers. Time series analysis –components and methods for their measurement, Vital statistics –birth, death and fertility rates, gross and net reproduction rates ,elements of life table


Books recommended for semester I & II

1. Fundamentals of Statistics Vol-I : Goon Gupta Dasgupta

2. Fundamentals of Mathematical Statistics: SC Gupta & VK Kapoor

3. Mathematical Statistics: Kapoor & Saxena

4. Mathematical Statistics: OP Gupta & BD Gupta

5. Fundamentals of Statistics Vol-II : Goon Gupta Dasgupta

6. Fundamentals of Applied Statistics: SC Gupta & VK Kapoor

SEMESTER III

PAPER I: STATISTICAL INFERENCE Point Estimation: Estimators and Estimate, Properties of estimators: Unbiasedness, Consistency and Efficiency, Sufficient statistics. Methods of estimation Interval Estimation: concept of best confidence intervals Test of hypothesis: Types of Hypothesis, errors of two kinds, significance level ,

power function of a test, Neyman -Pearson Lemma and its application in

finding most powerful tests for simple hypothesis against simple alternatives.

PAPER II: SAMPLING DISTRIBUTIONS AND TESTS FOR SIGNIFICANCE Sampling distribution: derivation and properties of chi-square, t and F distributions, Fisher’s Z-transformation Tests for significance: Large sample tests, Small sample tests, Tests of significance based on the above sampling distributions PAPER III: PRACTICAL BASED ON PAPER I & II

SEMESTER IV

PAPER I: SAMPLE SURVEY AND TECHNIQUES

Sampling vs complete enumeration, sampling units and frame, sampling and non-sampling errors, precision and efficiency of sampling estimators. Simple random sampling with and without replacement, use of random number tables, estimation of population mean and proportion by this method. Stratified random sampling, proportional and optimum allocation. Systematic sampling. Ratio and regression methods of estimation in simple random sampling PAPER II: ANALYSIS OF VARIANCE AND DESIGN OF EXPERIMENT

ANALYSIS OF VARIANCE: One way classification and two way classification with one observation per cell. DESIGN OF EXPERIMENT: Principles of design of experiments-Replication Randomization and Local control. Completely randomized design, Randomized Block Design and Latin Square Design. Missing plot techniques


Books recommended for semester III & IV



3. Mathematical Statistics: Kapoor & Saxena

4. Mathematical Statistics: OP Gupta & BD Gupta

1. Fundamentals of Statistics Vol-II: Goon Gupta Dasgupta


3. Sampling Techniques: WG Cochran

4. Design & Methods of Sample Surveys: Daroga Singh & FS Chaudhary

SEMESTER V

PAPER I: NON PARAMETRIC METHODS Order statistics and their distributions, Nonparametric tests and their applications( without derivations). Tests for Randomness, Test for Goodness of fit, one sample test- Sign test and Wilcoxon signed rank test. Two sample tests- Run tests, Kolmogorov Smirnov test, Median test and Mann Whitney U-test

PAPER II: MULTIVARIATE ANALYSIS

Multivariate Normal Distribution and its properties. Maximum likelihood

estimators of its parameters. Distribution of sample mean and sample Co-

variance matrix(without proof).

Linear regression model, least square theory, estimation of parameters and

test of hypothesis in a Linear model.


SEMESTER VI

PAPER I: QUALITY CONTROL

Control charts for variables and attributes:( �̅�,R), (�̅�, ), R , c, p and d charts

Sampling inspection by attributes- single and Double sampling plans,

producer’s and consumer’s risk, OC, ASN, AOQL and LTPD of sampling plans.

PAPER II: NUMERICAL ANALYSIS

Finite difference and interpolation, interpolation for equal and unequal interval – Newton’s forward and backward formula, Lagrange’s interpolation formula, Newton’s divided difference formula, Central difference formula: Newton- Gauss forward and backward formula, Stirling & Bessel’s formula Numerical integration- Trapezodial rule, Simpson’s rule and Weddle’s rule. PAPER III: PRACTICAL BASED ON PAPER I & II

Books recommended for semester V & VI



3. Fundamentals of Statistics Vol-II : Goon Gupta Dasgupta


5. Non Parametric Statistics for the Behavioural Sciences: Sidney Siegel &

Nathan Castallan Jr.

6. Multivariate Analysis- Theory & Applications : KC Bhuyan

ba/bsc course in statistics - kumaun universitykunainital.ac.in/forms/static/syallabus for ba...

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