MMT-008-material

MMT-008 Probability and Statistics (8 Credits)

This course “Probability and Statistics” is a 8-credit course on Stochastic Processes and Multivariate Analysis. IGNOU undergraduate course “Probability and Statistics” (MTE-11) is a prerequisite for this course. The course consists of eight blocks. The first four blocks of this course are presented to bridge the gap between the theory and applications of stochastic processes. The proofs of theorems which are either too involved or do not help in understanding concepts are omitted. The theorems are supported with applications. In the last four blocks, multivariate analysis has been presented which includes the practical component. This deals with the observation and analysis of two or more than two statistical variables at a time. The practical assignments session-wise are given at the end of corresponding units.

Block 1: Markov Chains

Unit 1 Conditional Probability

Unit 2 The Basics of Markov Chains

Unit 3 Stationary Markov Chains

Block 2: Markov Processes with Countable State Space

Unit 4 Branching Processes

Unit 5 Continuous Time Markov Processes I

Unit 6 Continuous Time Markov Processes I

Block 3: Renewal Processes

Unit 7 Renewal Processes I

Unit 8 Renewal Processes II

Unit 9 Renewal Processes III

Unit 10 Renewal Processes IV

Block 4: Queueing Theory

Unit 11 Poisson Queues

Unit 12 Non Poisson Queues

Unit 13 Network of Queues

Block 5: Basics of Multivariate Normals(MVN)

Unit 14 Some Linear Algebra

Unit 15 Definition and Properties of MVN I

Unit 16 Definition and Properties of MVN II

Block 6: Distributions Associated with MVN

Unit 17 Distribution of Correlation Coefficients

Unit 18 Orthogonal Transformations

Unit 19 Inference I

Unit 20 Inference II

Block 7: Applications of MVN

Unit 21 Inference III

Unit 22 Inference IV

Unit 23 Applications of MVN

Block 8: Additional Applications of MVN

Unit 24 Principal Component Analysis

Unit 25 Factor Analysis

Unit 26 Canonical Correlation Analysis

Unit 27 Conjoint Analysis