BA STATISTICS

BA STATISTICS

PAPER I : Probability and Statistical Methods-I
Important concepts in probability, classical, relative frequency and
axiomatic approaches to probability and their merits and demerits, conditional probability, independence of events, additive and multiplicative laws of probability for two events only, Bayes theorem and its applications.
Discrete and continuous random variables, probability mass/density
functions, mathematical expectation and its properties, moments, moment
generating function, measures of central tendency, measures of dispersion,
skewness and kurtosis.
Concept of bivariate, marginal and conditional distributions, correlation
and regression for two variables, rank correlation, method of least squares and fitting of curves.
Standard univariate discrete and continuous distributions: Binomial,
Hypergeometric, Geometric, Negative Binomial, Poisson and Normal and their properties.

PAPER II : Probability and Statistical Methods - II
Chebyshev s inequality. Weak law of large numbers. Strong law of
large numbers (statement only), Central limit theorem for independent identically distributed random variables with finite variance and its applications.
Parameter and statistic. Sampling distribution. Standard error, Sampling
distributions of sample mean and sample variance for normal distribution,
sampling distributions of t, F and chi-square statistics and tests of significance based on them, Large sample tests for single proportion and difference of two proportions, single mean and difference of two means, standard deviation.
Simple numerical problems based on t, F, chi-square and large sample tests. Transformation of random variables.

PAPER III : (Any one of the following two optional papers)
Option (i) : Statistical Inference, Regression Analysis and Design of
Experiments Point estimation, requirement of a good estimator - consistency, unbiasedness, efficiency and sufficiency. Cramer-Rao inequality, minimum variance unbiased estimators, method of maximum likelihood, confidence intervals (assuming normality) for means, proportions, difference of means and of proportions.

Statistical hypothesis, critical region, two kinds of errors, level of
significance and power of a test, Neyman-Pearson lemma (statement only),
critical regions for simple hypotheses. Sign test and run test.
Fitting a straight line in matrix terms, variance and covariance of bo
and bi from the matrix calculations, Bivariate and multiple linear regression.
Linear models, Best linear unbiased estimator (BLUE),. Gauss-Markov theorem, estimation of error variance.
Analysis of variance in one-way and two-way classified data with
equal number of observations per cell, Basic principles of experimental designs, completely randomised, randomised block and latin square designs.

Option (ii) : Applied Statistics
Time Series and its components with illustrations, additive and
multiplicative models, determination of trend by method of least squares,
measurement of seasonal fluctuations by ratio to trend method.
Sources of demographic data, measures of fertility and mortality,
standardised death rate, total fertility rate, gross reproduction rate, net
reproduction rate, life tables and its features and applications.
Process and product control, producer’s and consumer’s risks, control
charts for variables and attributes - X, R and p.
Need for sampling, principle steps in the conduct of sample surveys,
simple random sampling, stratified random sampling, systematic sampling, ratio and regression methods of estimation.