Statistics (Code No. 29)
I. Probability :
Classical and axiomatic definitions of probability, simple theorems on probability with examples, conditional probability, statistical independence, Bayes' theorem. Discrete and continuous random variables, probability mass function and probability density function, cumulative distribution function, joint marginal and conditional probability distributions of two variables, Expectation of functions of one and two random variables, moments, moment generating function, Binomial : Poisson Hypergeometric, Negative Binomial , Uniform, exponential, gamma, beta, normal probability distributions, Chebichev's inequality. Convergence in probability, weak law of large numbers, simple form of central limit therorem.
II. Statistical Methods :
Compilation, classification, tabulation and diagrammatic representation of statistical data, measures of central tendency, dispersion, skewness and kurtosis; measures of association and contingency, correlation and linear regression involving two variables, correlation ratio, curve fitting.
Concept of random sample and statistic sampling distribution of Chi-square, 't' and F statistics, their properties and tests of significance based on them. Large Sample Tests. Order statistics and their sampling distribution in case of uniform and exponential parent distribution.
III. Statistical Inference :
Theory of estimation : unbiasedness, consistency, efficiency, sufficiency, Crammer-Rao Lower bound, best linear unbiased estimates, methods of estimation, methods of moments, maximum likelihood, leastsquares, minimum, Chi-square, properties of maximum likelihood estimators (without proof), simple problems of constructing confidence intervals for parameters of normal distribution.
Testing of hypothesis, simple and composite hypothesis, Statistical test, two kinds of errors, Best critical regions for simple verses simple hypothesis concerning one parameter of binomial, Poission, uniform, exponential and normal distribution. Non parametric tests: Chi-square, sign, run median tests, Wilcoxon test, rank correlation methods.
IV. Sampling Theory and Design of Experiments :
Principles of sampling, frame and sampling units, sampling and non-sampling errors, simple random sampling, stratified sampling, cluster sampling, systematic sampling, ratio and regression estimates designing of sample surveys with reference to recent large scale surveys in India.
Analysis of Variance with equal number of observations per cell in one, two and three way classification, transformations to stabilize variance. Principles of experimental design, completely randomized design Randomized block design, Latin square design, Missing plot technique, 23 factorial experiments.
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