Statistics

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.