Unit – I : Probability Theory
Unit – II : Probability Distributions
- Discrete probability distributions–Binomial, Poisson, Negative Binomial, Hypergeometric and Multinomial distributions.
- Continuous probability distributions–Exponential, Normal, Uniform, Beta, Gamma, Cauchy and Bivariate Normal distributions.
Unit – III : Statistical Methods
Frequency distribution, graphical and diagrammatic representation of data. Measures of location and dispersion, moments, skewness and kurtosis. Curve fitting, association of attributes. Simple correlation and regression, partial and multiple correlations and regressions, correlation ratio. Distribution of sample mean; t , F and Chi-square distributions.
Unit – IV : Estimation and Testing of Hypothesis
Characteristics of a good estimator. Estimation by the methods of maximum likelihood and least squares, properties of maximum likelihood estimator, Cramer-Rao inequality, sufficient statistic and Rao-Blackwell theorem. Interval estimation. Testing of simple and composite hypotheses, types of errors, critical region. Neyman- Pearson fundamental lemma, power function, MP and UMP tests. Non-parametric tests- Sign, median and run tests, large sample tests, tests based on , and Chi-square distributions
Unit – V : Sampling Techniques and Designs of Experiments
Census versus sample surveys. Simple random sampling, stratified sampling, systematic sampling, sampling with probability proportional to size. Ratio and regression methods of estimation. Principles of designs of experiment. Lay out and analysis of completely randomized, randomized block and Latin square designs. Factorial experiments (2² , 2³ and 3² experiments), Confounding (total and partial).