CCMAS Course Search

Sample space; algebra of sets and events; axiomatic definition of probability and independence; Bayes theorem; Random variables and their distributions; Moment; Cumulant and Probability Generating functions; Some special distributions and their properties; Multivariate continuous distribution: Marginal and Conditional Distribution; Distribution functions of random variables and some derived distributions; Limiting theorems and limiting distributions; Elements of stochastic processes

Introduction to measure theoretic probability; derivation and transformation of probability distributions; generating functions and characteristic functions; conditional expectation; sufficiency; and unbiased estimation; methods of large sample theory including laws of large numbers and central limit theorems; order statistics

Analysis and control of variations in a production process; OC of a control chart; Control charts for attributes and variables; Cumulative sum control charts; Other control charts; Methods of controlling several related characteristics; Process capability analysis; Design of control charts; Specification and Tolerance

Construction and choice of strata; frames and various equal and unequal probability sampling schemes with properties; Estimation of means; proportion and their variances; Successive sampling scheme; Problems of non-sampling error and non-response: application to some selected specialized survey

The design and use of existing statistical software; methods of simulation of random processes; numerical methods of fitting linear models; multivariate analysis; methods for nonlinear modeling; Introduction of key aspects of statistical consulting and data analysis activities; report writing and presentation

Conditioning; distribution theory; approximation to distributions; modes of convergence; limit theorems; statistical models; parameter estimation; properties of estimators; confidence sets; theory of hypothesis tests; introduction to Bayesian inference and nonparametric estimation

Classification of stochastic processes; Random walk models; markov chains; inventory model; branching processes; Poisson; birth-and-death processes; Waiting time models; Estimation problems

Theory of stochastic models and their forecasting; Model building: identification; estimation; Diagnostic checking; Analysis of stationary Data Co-integration and error correction techniques