MA204
INTRODUCTION TO PROBABILITY THEORY
Objectives
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To introduce the fundamental concepts and theorems of probability theory
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To apply elements of stochastic processes for problems in real life
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To understand elementary queuing concepts and apply elsewhere in computer science.
Outcomes
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Conceptualize the necessity of randomness concept in practical situation
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Approximate the real problems using stochastic process and deduce results
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Deduce useful results and interpret them based on the analysis of queuing theory
Unit – I
Axioms of probability theory- Probability spaces - Joint and conditional probabilities- Bayes’ Theorem- Independent events.
Unit – II
Random Variable and random vectors -Distributions and densities. Independent random variables – Functions of one and two random variables.
Unit – III
Moments and characteristic functions- Inequalities of Chebyshev and Schwartz. Convergence concepts.
Unit – IV
Random processes- Stationarity and ergodicity - Strict sense and wide sense stationary processes - Covariance functions and their properties - Spectral representation - Wiener-Khinchine theorem.
Unit – V
Gaussian processes - Processes with independent increments - Poisson processes - Lowpass and Bandpass noise representations.
TEXT BOOKS
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Davenport, Probability and Random Processes for Scientist and Engineers, McGraw-Hill
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Papoulis, A., Probability, Random variables and Stochastic Processes, McGraw Hill.