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Statistics
Note: In all nine questions will be set with two questions from each of
the Sections A, B and C, and three questions from Section D.
A candidate will be required to answer five questions, selecting at least
one from each section. All questions will carry equal marks.
(a) Probability Theory:
Random Experiments; Classical and Axiomatic Definitions of Probability; Addition
and Multiplication Theorems; Conditional Probability; Independence of Events;
Bay's Theorem.
Random Variables; Probability Mass and Density Functions; Distribution Functions;
Mathematical Expectation. Moments; Moment Generating Functions.
Binomial, Poisson, Geometric, Hypergeometric; Negative Binomial, Uniform,
Normal, Beta and Gamma Distributions. Bivariate Normal distributions; Conditional
and Marginal distributions.
Chebychev's Inequality; Weak Law of Large Numbers and Central Limit Theorem
for Independently and Identically Distributed Random Variables (statements
and applications only)
(b) Statistical Methods:
Compilation and Summarization of data. Graphical and Diagrammatic Representation.
Central Tendency and its measures; Arithmetic Mean, Geometric Mean, Harmonic
Mean, Median and Mode: their relative merits and demerits. Dispersion and
its measures; Range, Inter-quartile Range, Standard Deviation, Mean Absolute
Deviation and Coefficient of Variation; Their Properties.
Skewness and Kurtosis, and their measures. Summarization of Bivariate data;
Consistency of Qualitative data; Independence of Attributes and Measures of
Association.
Correlation and Regression. Rank Correlation. Inter-class Correlation; Correlation
Ratio; Partial and Multiple Correlations for the case of three characteristics
only.
(c) Sampling Distributions and Inference:
Concept of Random Sampling and Sampling Distribution: t, X2 (Chi-square),
F- and Z-distributions.
Testing of Hypothesis: Two types of errors; Level of significance; Power;
Norman-Pearson Lemma for simple hypothesis against a simple alternative; Concept
of most powerful test and UMP test.
Test based on normal, t, Z2 (Chi-square) and F-distributions for proportions,
means, variances, correlation and regression coefficients; Large sample tests.
Non-parametric tests; Sign Test; Median Test; Wilcoxon-Mann-Whitney Test;
Run Test. Estimation of parameters; Point and Interval estimation; Unbiasedness,
Consistency, Efficiency and Sufficiency of Estimators. Methods of Maximum
Likelihood and Moments: Their properties (Statements only).
(d) Applied Statistics:
Sampling vs. Complete Enumeration; Simple Random, Sampling, Cluster Sampling
and two Stage Sampling with Numbers.
Stratified Sampling: Problems of Allocation. Systematic Sampling; Cluster
Sampling and Two-Stage Sampling with Equal Primary Stage Units, Ratio and
Regression. Methods of Estimation.
Non-sampling errors; Interpenetrating Sub-samples. Design of Experiments;
Principles of Scientific Experimentation; Randomization, Replication and Local
Control; Completely Randomized; Randomized Block and Latin Square Designs;
Missing Plot Technique.
Time Series Analysis: Components of a Time Series; Measurement of Trend, Seasonal
Variations and Random Fluctuations.
Statistical Quality Control: Causes of Variation; Control and Specification
Limits; Construction and Uses of X, R, P, s and C charts.
Single and Double Acceptance, Sampling Plans.
Index Number; Definition. Construction and Uses of Price and quantity Index
Numbers. Laspeyre, Paasche, Marshall Edgeworth and Fisher Index Numbers; Tests
for Index Numbers.
Construction of Cost of Living Index Numbers.
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