### MA8451 - PROBABILITY AND RANDOM PROCESSES (Syllabus) 2017-regulation Anna University

## MA8451 - PROBABILITY AND RANDOM PROCESSES (Syllabus) 2017-regulation Anna University

MA8451 |
PROBABILITY AND RANDOM PROCESSES |
LPTC |
---|

**3003**

**OBJECTIVES:**

• To provide necessary basic concepts in probability and random processes for applications such as random signals, linear systems in communication engineering.

• To understand the basic concepts of probability, one and two dimensional random variables and to introduce some standard distributions applicable to engineering which can describe real life phenomenon.

• To understand the basic concepts of random processes which are widely used in IT fields.

• To understand the concept of correlation and spectral densities.

• To understand the significance of linear systems with random inputs.

• To understand the basic concepts of probability, one and two dimensional random variables and to introduce some standard distributions applicable to engineering which can describe real life phenomenon.

• To understand the basic concepts of random processes which are widely used in IT fields.

• To understand the concept of correlation and spectral densities.

• To understand the significance of linear systems with random inputs.

UNIT I |
PROBABILITY AND RANDOM VARIABLES |
12 |
---|

Probability – Axioms of probability – Conditional probability – Baye‘s theorem - Discrete and continuous random variables – Moments – Moment generating functions – Binomial, Poisson, Geometric, Uniform, Exponential and Normal distributions.

UNIT II |
TWO - DIMENSIONAL RANDOM VARIABLES |
12 |
---|

distributions – Marginal and conditional distributions – Covariance – Correlation and linear regression – Transformation of random variables – Central limit theorem (for independent and identically distributed random variables).

UNIT III |
RANDOM PROCESSES |
12 |
---|

Classification – Stationary process – Markov process - Markov chain - Poisson process – Random telegraph process.

UNIT IV |
CORRELATION AND SPECTRAL DENSITIES |
12 |
---|

Auto correlation functions – Cross correlation functions – Properties – Power spectral density – Cross spectral density – Properties.

UNIT V |
LINEAR SYSTEMS WITH RANDOM INPUTS |
12 |
---|

Linear time invariant system – System transfer function – Linear systems with random inputs – Auto correlation and cross correlation functions of input and output.

**TOTAL: 60 PERIODS**

**OUTCOMES: Upon successful completion of the course, students should be able to:**

• Understand the fundamental knowledge of the concepts of probability and have knowledge of standard distributions which can describe real life phenomenon.

• Understand the basic concepts of one and two dimensional random variables and apply in engineering applications.

• Apply the concept random processes in engineering disciplines.

• Understand and apply the concept of correlation and spectral densities.

• The students will have an exposure of various distribution functions and help in acquiring skills in handling situations involving more than one variable. Able to analyze the response of random inputs to linear time invariant systems.

• Understand the basic concepts of one and two dimensional random variables and apply in engineering applications.

• Apply the concept random processes in engineering disciplines.

• Understand and apply the concept of correlation and spectral densities.

• The students will have an exposure of various distribution functions and help in acquiring skills in handling situations involving more than one variable. Able to analyze the response of random inputs to linear time invariant systems.

**TEXT BOOKS:**

1. Ibe, O.C.," Fundamentals of Applied Probability and Random Processes ", 1st Indian Reprint, Elsevier, 2007.

2. Peebles, P.Z., "Probability, Random Variables and Random Signal Principles ", Tata McGraw Hill, 4th Edition, New Delhi, 2002.

2. Peebles, P.Z., "Probability, Random Variables and Random Signal Principles ", Tata McGraw Hill, 4th Edition, New Delhi, 2002.

**REFERENCES:**

1. Cooper. G.R., McGillem. C.D., "Probabilistic Methods of Signal and System Analysis", Oxford University Press, New Delhi, 3rd Indian Edition, 2012.

2. Hwei Hsu, "Schaum‘s Outline of Theory and Problems of Probability, Random Variables and Random Processes ", Tata McGraw Hill Edition, New Delhi, 2004.

3. Miller. S.L. and Childers. D.G., ―Probability and Random Processes with Applications to Signal Processing and Communications ", Academic Press, 2004.

4. Stark. H. and Woods. J.W., ―Probability and Random Processes with Applications to Signal Processing ", Pearson Education, Asia, 3rd Edition, 2002.

5. Yates. R.D. and Goodman. D.J., ―Probability and Stochastic Processes", Wiley India Pvt. Ltd., Bangalore, 2nd Edition, 2012.

2. Hwei Hsu, "Schaum‘s Outline of Theory and Problems of Probability, Random Variables and Random Processes ", Tata McGraw Hill Edition, New Delhi, 2004.

3. Miller. S.L. and Childers. D.G., ―Probability and Random Processes with Applications to Signal Processing and Communications ", Academic Press, 2004.

4. Stark. H. and Woods. J.W., ―Probability and Random Processes with Applications to Signal Processing ", Pearson Education, Asia, 3rd Edition, 2002.

5. Yates. R.D. and Goodman. D.J., ―Probability and Stochastic Processes", Wiley India Pvt. Ltd., Bangalore, 2nd Edition, 2012.

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