## Course Detail

 Course Name Probability and Random Processes Course Code 19MAT205 Program B. Tech. in Electronics and Computer Engineering Semester 4 Year Taught 2019

### Syllabus

##### 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.

### Objectives and Outcomes

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

 PO/PSO/ CO PO1 PO2 PO3 PO4 PO5 PO6 PO7 PO8 PO9 PO10 PO11 PO12 PSO1 PSO2 CO1 3 2 3 CO2 3 3 3 CO3 3 3 2 CO4 3 2 2 CO5 2 2 2

### Textbook / Reference

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)

 Assessment Internal External Periodical 1 (P1) 15 – Periodical 2 (P2) 15 – *Continuous Assessment (CA) 20 – End Semester – 50 *CA – Can be Quizzes, Assignment, Projects, and Reports.

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