Statistics

Descriptive statistics

Exploratory data analysis

Sample space

Discrete probability

Independent events

Bayes theorem

Random variables and distribution functions (univariate and multivariate)

Expectation and moments

Independent random variables

Marginal and conditional distributions

Characteristic functions

Probability inequalities (Tchebyshef, Markov, Jensen)

Modes of convergence

Weak and strong laws of large numbers

Central Limit theorems (i.i.d. case)

Markov chains with finite and countable state space

Classification of states

Limiting behaviour of n-step transition probabilities

Stationary distribution

Poisson and birth-and-death processes

Standard discrete and continuous univariate distributions

Sampling distributions

Standard errors and asymptotic distributions

Distribution of order statistics and range

Methods of estimation

Properties of estimators

Confidence intervals

Tests of hypotheses

Most powerful and uniformly most powerful tests

Likelihood ratio tests

Analysis of discrete data and chi-square test of goodness of fit

Large sample tests

Simple nonparametric tests for one and two sample problems

Rank correlation and test for independence

Elementary Bayesian inference

Gauss-Markov models

Estimability of parameters

Best linear unbiased estimators

Confidence intervals

Tests for linear hypotheses

Analysis of variance and covariance

Fixed, random and mixed effects models

Simple and multiple linear regression

Elementary regression diagnostics

Logistic regression

Multivariate normal distribution

Wishart distribution and their properties

Distribution of quadratic forms

Inference for parameters

Partial and multiple correlation coefficients and related tests

Data reduction techniques

Principle component analysis

Discriminant analysis

Cluster analysis

Canonical correlation

Simple random sampling

Stratified sampling and systematic sampling

Probability proportional to size sampling

Ratio and regression methods

Completely randomized designs

Randomized block designs and Latin-square designs

Connectedness and orthogonality of block designs

BIBD

2 K factorial experiments: confounding and construction

Hazard function and failure rates

Censoring and life testing

Series and parallel systems