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GRADUATE DEGREE STANDARD |
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1. 1 PROBABILITY
Sample space and events, Probability measures and probability
space-Random variables, Disorete and Continious random
Variables, probability density and distribution functions.
Simple theorems on Probability. Marginal and Conditional
distributions, Expectations and moments, Independence
of events, Moments and Cumulants generating functions.
Borel - Cantelli lemma, characteristic function.
1. 2 CONVERGENCE
OF RANDOM VARIABLES
Convergence in probability, almost sure, everywhere
and in distribution - Weak law and strong law of large
numbers, central limit theorem -(Lindeberg - Levy, Liapounor's,
Lindoberg - Feller's). Tchebycher's inequality and Clivenko
- Cantelli theorem.
1. 3 DISCRETE DISTRIBUTIONS
Uniform Binomial, Poisson, Negative - Binomial, Hypergeometric
Distribution.
1. 4 CONTINUOUS DISTRIBUTIONS
Uniform, Normal, Cauchy, Beta, Gamma, Log - Normal Exponential,
Weibull distributions.
1. 5 ESTIMATION
Point estimation - Interval estimation - Properties
of estimates - Consistency, Unibiasedness effeciency
sufficiency and Completeness, Fisher - Neyman Factorisation
and Rao - Blackwell Theorems, Lehman - Scheffe theorem,
Cramer - Rae inequality, method of maximum likelihood
estimate and its properties, method of momentsm Chi
- square and Principles of least square.
1. 6 TESTING OF HYPOTHESIS
Simple and Composite Hypothesis, two kinds of erors,
power functions, most powerful test, Neyman - Pearson
Lemma UMP and unbiased test, MLR property and its use
for construction of UMP tests, Likelihood ratio test,
Confidence intervals for large and small samples.
1. 7 NON - PARMETRIC
TESTS
Tests for goodness of fit, Chi - Square and kolmogrov
test. Ram test for Randomness, Median test, sign test
for location, Wilcoxin - Mannwhitney U - test and Kolmogrov
- Smirnov test for two sample problem sequential test,
wald SPRT test.
1. 8 LINEAR MODELS
Theory of Least squares, classification of linear models,
Best linear unbiased estimaters (BLUE) for Gauss - Markovs
Conditions - Estimable functions, Test of linear hypothosis
and its applications to ANOVA.
1. 9 MULTIVARIATE
ANALYSIS
Multiple and partical correlations, Regression, Marginal
and Conditional Distribution functions, MLE of mean
vector and dispersion matrix for multivariate Normal.
Mahalonobis D2 and Hotelling T2 statistic and their
applications (Excluding derivation of distributions)
Fisher's Discreminant analysis, Wishart Distribution
(Excluding Derivation of distribution) and its properties.
Factor analysis and Principle Component analysis.
1. 10 BASIC PROGRAMMING
Variables, Constants, Strings, flow charts, Basic expression
and control statements, standard Library functions,
subsevipted Variables. DIM and DATA statements, Simple
programming problems - FORTRAN Language - Simple illustrations,
Simple WORD STAR and LOTUS Commands.
PAPER - II
2.1 DESIGN OF EXPERIMENTS:-
Principles, CRD, RBD, LSD, RBD with many observations
per cell, missing plot techinque, fractional experiments
2" and 3" design. General theory of partial
Confounding and fractional replication, analysis of
Split plot, BIBD and PBIBD, simple lattice design, lineer
and second order response surface design and Youden
Square Design.
2.2 STATISTICAL QUALITY
CONTROL:-
Concepts of quality and meaning of Control Different
types of Control Charts like x, R, p and np charts and
it uses. CUSUM chart. Sampling inspection Vs 100 percent
inspection, single, double, multiple and sequential
plans for attribes inspection. Variable sampling plan.
The OC, ASN, ATI and AOQ Curves, concept of producer's
risk and Consumer's risk, AQL, LTPD, AOQL, IQL, MAPD
and MAAOQ.
2.3 RELIABILITY :-
Definition of Reliability; maintainability and availability,
Life distribution, failure rate and bath-tub, failure
cure exponential and wleibull model. Reliability of
series and parallel systems and other simple Configurations.
Different types of redundancy like hot and cold and
use of redundancy in reliability improvement. Problems
in life testing, Censored and truncated experiments
for exponential models.
2.4 SAMPLING:-
Simple random sampling systematic and stratified, Ratio
and Regression estimates, Double sampling, Sampling
and Non-Sampling errors. Cluster sampling, Two stage
and Multistage sampling Multi-phase sampling Sample
survey organisation - CSO and NSSO.
2.5 OPERATIONS RESEARCH
:-
Linear Programming-Simplex procedure, Transportation
and Assignment problems, Duality, Dual Simplex, Game
Theory, Single and Multi period inventory Control Models-ABC
analysis, Queuing Models - Waiting time distributions
of M/M/1, M/M/C Models with different service policy,
Service time distributions.
2.6 TIME SERIES :-
Concepts of time series, additive and multiplicative
models, resolutions into Components, determination of
trend by free hand drawing, Moving averages, filling
of mathematical Curves, seasonal indices and the estimate
of the variance for random Components, Auto-regressive,
Moving averages and ARIMA models.
2.7 INDEX NUMBERS:-
Definition, Construction interpretation and limitations
of index numbers, Lapeyre's Paasche'sMarshell - Edgeworth,
Fisher's index numbers and their Comparisons for Good
index Number. Construction for cost of living index
number and Wholesale price index.
2.8 ECONOMETRICS
:-
Theory and analysis of Consumer demand specification
and estimation of demand function, Demand elasticities.
Thery of production, supply functions and elasticities,
input demand functions. Estimation of parameters in
Single equation model classical least squares, generalised
least squares, heteroscedasticity, serial correlation,
multi collineavity, errors in variables model, simultaneous
equation models, Input and output models, Identification,
Rank an Order Conditions, Short-term-economic forecasting.
2.9 STOCHASTIC PROCESSES
:-
Concepts, homogeneous discrete time markov Chains-illustrations.
TPM Classification of states and Chains, higher transition
probabilities, stability of Markov Chain, limiting behaviour,
one Dimensional Random Walk. Chapman-kolmogrov equation,
Ergodic theorem, Poission Processes and related distributions,
Birth Process, Death Processes, Brith-Death Processes.
2.10 DEMOGRAPHY:-
Vital Statistics, birth and death ratio, rates and life
table, sources of demographic data, NSS and other demographic
surveys, Limitations and uses of data, Logistic and
other population growth curves, GROSS and NET Reproduction
rates, Morbidity and Mortality rates
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