MA1254 RANDOM PROCESSES 3 1 0 100
AIM
This course aims at providing the necessary basic concepts in random processes. A knowledge of fundamentals and applications of phenomena will greatly help in the understanding of topics such a estimation and detection, pattern recognition, voice and image processing networking and queuing.
OBJECTIVES
At the end of the course, the students would
• Have a fundamental knowledge of the basic probability concepts.
• Have a well – founded knowledge of standard distributions which can describe real life phenomena.
• Acquire skills in handling situations involving more than one random variable and functions of random variables.
• Understand and characterize phenomena which evolve with
respect to time in probabilistic manner.
• Be able to analyze the response of random inputs to linear time invariant systems.
UNIT I PROBABILITY AND RANDOM VARIABLE 9 +3
Axioms of probability - Conditional probability - Total probability – Baye’s theorem - Random variable - Probability mass function - Probability density functions- Properties –Moments - Moment generating functions and their properties.
UNIT II STANDARD DISTRIBUTIONS 9 +3
Binomial, Poisson, Geometric, Negative Binomial, Uniform, Exponential, Gamma, Weibull and Normal distributions and their properties - Functions of a random variable.
UNIT III TWO DIMENSIONAL RANDOM VARIABLES 9 + 3
Joint distributions - Marginal and conditional distributions – Covariance - Correlation and regression - Transformation of random variables - Central limit theorem.
UNIT IV CLASSIFICATION OF RANDOM PROCESSES 9 + 3
Definition and examples - first order, second order, strictly stationary, wide – sense stationary and Ergodic processes - Markov process - Binomial, Poisson and Normal processes - Sine wave process.
UNIT V CORRELATION AND SPECTRAL DENSITIES 9 + 3
Auto correlation - Cross correlation - Properties – Power spectral density – Cross spectral density - Properties – Wiener-Khintchine relation – Relationship between cross power spectrum and cross correlation function - Linear time invariant system - System transfer function –Linear systems with random inputs – Auto correlation and cross correlation functions of input and output.
TUTORIAL 15
TOTAL : 60
TEXT BOOKS
1. Ross, S., “A First Course in Probability”, Fifth edition, Pearson Education, Delhi, 2002.
2. Peebles Jr. P.Z., “Probability Random Variables and Random Signal Principles”, Tata McGraw-Hill Pubishers, Fourth Edition, New Delhi, 2002. (Chapters 6, 7 and 8).
REFERENCES
1. Henry Stark and John W. Woods “Probability and Random Processes with Applications to Signal Processing”, Pearson Education, Third edition, Delhi, 2002.
2. Veerarajan. T., “Probabilitiy, Statistics and Random process”, Tata McGraw-Hill Publications, Second Edition, New Delhi, 2002.
3. Ochi, M.K. , “Applied Probability and Stochastic Process”, John Wiley & Sons, New York, 1990.
AIM
This course aims at providing the necessary basic concepts in random processes. A knowledge of fundamentals and applications of phenomena will greatly help in the understanding of topics such a estimation and detection, pattern recognition, voice and image processing networking and queuing.
OBJECTIVES
At the end of the course, the students would
• Have a fundamental knowledge of the basic probability concepts.
• Have a well – founded knowledge of standard distributions which can describe real life phenomena.
• Acquire skills in handling situations involving more than one random variable and functions of random variables.
• Understand and characterize phenomena which evolve with
respect to time in probabilistic manner.
• Be able to analyze the response of random inputs to linear time invariant systems.
UNIT I PROBABILITY AND RANDOM VARIABLE 9 +3
Axioms of probability - Conditional probability - Total probability – Baye’s theorem - Random variable - Probability mass function - Probability density functions- Properties –Moments - Moment generating functions and their properties.
UNIT II STANDARD DISTRIBUTIONS 9 +3
Binomial, Poisson, Geometric, Negative Binomial, Uniform, Exponential, Gamma, Weibull and Normal distributions and their properties - Functions of a random variable.
UNIT III TWO DIMENSIONAL RANDOM VARIABLES 9 + 3
Joint distributions - Marginal and conditional distributions – Covariance - Correlation and regression - Transformation of random variables - Central limit theorem.
UNIT IV CLASSIFICATION OF RANDOM PROCESSES 9 + 3
Definition and examples - first order, second order, strictly stationary, wide – sense stationary and Ergodic processes - Markov process - Binomial, Poisson and Normal processes - Sine wave process.
UNIT V CORRELATION AND SPECTRAL DENSITIES 9 + 3
Auto correlation - Cross correlation - Properties – Power spectral density – Cross spectral density - Properties – Wiener-Khintchine relation – Relationship between cross power spectrum and cross correlation function - Linear time invariant system - System transfer function –Linear systems with random inputs – Auto correlation and cross correlation functions of input and output.
TUTORIAL 15
TOTAL : 60
TEXT BOOKS
1. Ross, S., “A First Course in Probability”, Fifth edition, Pearson Education, Delhi, 2002.
2. Peebles Jr. P.Z., “Probability Random Variables and Random Signal Principles”, Tata McGraw-Hill Pubishers, Fourth Edition, New Delhi, 2002. (Chapters 6, 7 and 8).
REFERENCES
1. Henry Stark and John W. Woods “Probability and Random Processes with Applications to Signal Processing”, Pearson Education, Third edition, Delhi, 2002.
2. Veerarajan. T., “Probabilitiy, Statistics and Random process”, Tata McGraw-Hill Publications, Second Edition, New Delhi, 2002.
3. Ochi, M.K. , “Applied Probability and Stochastic Process”, John Wiley & Sons, New York, 1990.
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