(i) Probability: Classical and Statistical definitions of probability, Importance of the Concept of Probability, Calculation of Probability, Theorems of Probability, Simple theorem of probability with examples. Conditional probability and statistical independence Bayer theorem. Random variables- Discreet and continuous probability functions and probability density functions probability distributions in doreor more varieties. Mathematical
(ii) Statistical methods- Compilation classification, tabulation and diagrammatic representation of various type of statistical data. Concepts of statistical population land frequency curbs, measures of central tendency and despertions. Moment and commulants, Measure of skewness and Kurtosis Moments-generating function. Hyper-geometric
normal Negative Binominal Rectangular and log normal distributions General description of the Presonian system of curves.
(iii) Theoretical distribution, binomial, Poisson and Normal distribution. General properties of a bivariate distribution, bivariate normal distribution, measures of association and contingency, Correlation and Regression Analysis, Difference between correlation and Regression Analysis. Correlation and linear regression involving two or more variables. Correlation ratio inter class correlation Bank correlation, Non-linear regression analysis.
(iv) Sampling methods, basic of sampling types and importance of sampling. Sampling distribution and statistical inference—random sample, statistics concepts of sampling distribution and standard error. Derivation of sampling distribution of mean of independent normal varieties. X2-T and F statistics, their properties and uses. Derivation
of sampling, distribution of sample means variances and correlation coefficient from a bivariate normal population. Derivation (in large samples) and uses Personian X2.
(v) Theory of Estimation — Requirements of a good estimate/biasedness., consistency, efficiency and sufficiency Cramer-Rao bound to variance of estimates. Best linear unbiased estimates. Methods of estimation. General description of the methods of moments, methods of maximum likelihood of least squares and methods of minimum X2
properties of maximum likelihood estimators (without proof). Theory of confidence intervals, simple problems of setting confidence limits.
(i) Hypothesis; Meaning, Function, conditions for a valid Hypothesis, Formulation of Hypothesis, Types and Forms of Hypothesis, Theory of testing Hypotheses— Simple and composite hypothesis, statistical test and critical regions. Two kinds of error, level of significance and power of tests. Optimum critical regions for simple hypothesis
concerning one parameter. Construction of such regions for simples hypothesis relating to normal population.
(ii) Likelihood ratio tests— Tests involving mean, variance correlation and regression coefficients in unvariable and biveriate normal populations, Multiple regression, multiple and partial correlation. Simple non-parametric tests—sign, run-median, rank and randomization tests Sequential test of a simple hypotheses against a simple alternative (without derivation).
(iii) Need for statistical methods, steps in statistical method, sampling techniques, sampling versus complete enumeration, Principle of sampling, Frames and sampling units, Sampling and non-sampling description of multi-stage and multiphase sampling ratio and regression, methods of estimation. Designing of simple surveys and reference to recent large-scale surveys in India.
(iv) Linear statistical models, Theory of Least squares and Analysis of variance, Normal Equations, Least squares estimates and their precision, Test of significance, and interval estimates based on least squares theory in one-way, two-way and three-way classified data.
(v) Design of Experiments—Analysis of variance and coveriance with equal number of observation in “the cells” Transformation of variate to stabilize variance. Principle of experimental designs, completely randomized, randomized block and Latin square designs, missing plot techniques. Factorial experiments and confounding in 2s [s=2 (i) 51.3 and 33] designs. Split pot design, Balanced incomplete designs and simple lattice.