Statistics Syllabus

Note: The 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.