Course

Module I

Review of probability concepts – conditional probability- Bayes theorem. Random Variable and Distributions: Introduction to random variable – discrete and continuous random variables and its distribution functions- mathematical expectations – moment generating function and characteristic function.

Module II

Binomial, Poisson, Geometric, Uniform, Exponential, Normal distribution functions (moment generating function, mean, variance and simple problems) – Chebyshev’s theorem.

Module III

General concepts and definitions -stationary in random processes -strict sense and wide sense stationary processes – autocorrelation and properties- special processes – Poisson points, Poisson and Gaussian processes and properties- systems with stochastic inputs – power spectrum- spectrum estimation, ergodicity –Markov process and Markov chain, transition probabilities, Chapman Kolmogrov theorem, limiting distributions classification of states. Markov decision process.

Course Objectives

• To understand the concepts of basic probability and random variables.
• To understand some standard distributions and apply to some problems.
• To understand the concepts of random process, stationarity and autocorrelation functions.
• To understand markov process and markov chain and related concepts.

Course Outcomes

• CO1: Understand the basic concepts of probability and probability Modelling.
• CO2: Gain knowledge about statistical distributions of one and two dimensional random variables and correlations.
• CO3: Understand the basic concepts of stochastic processes and the stationarity.
• CO4: Understand the purpose of some special processes
• CO5: Gain knowledge about spectrum estimation and spectral density function

CO – PO Mapping

Textbook

• Douglas C. Montgomery and George C. Runger, Applied Statistics and Probability for Engineers, (2005) John Wiley and Sons Inc.
• A. Papoulis, and Unni krishna Pillai, “Probability, Random Variables and Stochastic Processes”, Fourth Edition, McGraw Hill, 2002.

References

• J. Ravichandran, “Probability and Random Processes for Engineers”, First Edition, IK International, 2015.
• Scott L. Miller, Donald G. Childers, “Probability and Random Processes”, Academic press, 2012.

Evaluation Pattern 50:50 (Internal: External)