# MA206

## Probability Theory and Random Process

Pre-Requisite: MA207
Contact Hours and Credits: (3-0- 0) 3

### Objective:

To expose the students to the basics of probability theory and random processes essential for their subsequent study of analog and digital communication.

### Topics Covered:

Axioms of probability theory. Probability spaces. Joint and conditional probabilities. Bayes’ Theorem- Independent events.

Random variables and random vectors. Distributions and densities. Independent random variables. Functions of one and two random variables.

Moments and characteristic functions. Inequalities of Chebyshev and Schwartz. Convergence concepts.

Random processes. Stationarity and ergodicity. Strict sense and wide sense stationary processes. Covariance functions and their properties. Spectral representation. Wiener-Khinchine theorem.

Gaussian processes. Processes with independent increments. Poisson processes. Low pass and Band pass noise representations.

### Course Outcomes:

Students will be able to

• CO1: Understand the axiomatic formulation of modern Probability Theory and think of random variables as an intrinsic need for the analysis of random phenomena.
• CO2: Characterize probability models and function of random variables based on single & multiples random variables.
• CO3: Evaluate and apply moments & characteristic functions and understand the concept of inequalities and probabilistic limits.
• CO4: Understand the concept of random processes and determine covariance and spectral density of stationary random processes.
• CO5: Demonstrate the specific applications to Poisson and Gaussian processes and representation of low pass and band pass noise models.

### Text Books:

• Davenport, Probability and Random Processes for Scientist and Engineers, McGraw-Hill.
• Papoulis, A., Probability, Random variables and Stochastic Processes, McGraw Hill.

### Reference Books:

• E.Wong : Introduction to Random Processes, Springer Verlag.
• W.A.Gardner: Introduction to Random Processes, (2/e), McGraw Hill.
• H. Stark & J.W. Woods: Probability, Random Processes and Estimations Theory for Engineers, (2/e), Prentice Hall.