**BM1201 TRANSFORMS AND RANDOM PROCESSES 3 1 0 100**

**1. FOURIER TRANSFORMS: 9**

Fourier transform pairs, Properties – Fourier Sine and Cosine transforms, Transforms of simple functions, Transforms of derivatives, Convolution integrals, Evaluation of integrals using Fourier Transform.

**2. LAPLACE TRANSFORM: 9**

Transforms of simple functions, Properties, Transforms of derivatives and integrals, Periodic functions, Convolution theorem, Inversion formula, Initial and Final value theorems,

Applications to solve ordinary differential equations.

**3. PROBABILITY AND RANDOM VARIABLES: 8**

Probability concepts, Random variables, Moments, Moment generating function, Binomial, Poisson, Geometric, Exponential, Gamma distributions, Functions of a random variable.

**4. TWO DIMENSIONAL RANDOM VARIABLES: 8**

Joint, Marginal and Conditional distributions, Covariance, Correlation and Regression.

**5. RANDOM PROCESSES: 11**

Classification, Stationary and Markov processes, Poisson Process – Properties, Pure Birth Process, Birth and Death Process, Markov Chain, Auto-correlation and Cross-correlation functions - Properties.

**L = 45, T = 15, TOTAL: 60**

**TEXT BOOKS:**

1. Kandasamy.P, Thilagavathy. K, Gunavathy.K, ‘Engineering Mathematics’ Vol.III S.Chand & Co.2002

2. Veerarajan.T, ‘Probability statistics and Random Processes’ Tata McGraw-Hill, Co, New Delhi.2002.

**REFERENCES:**

1. J. Medhi, ‘Stochastic Processes’, New Age International Publication, New Delhi (2nd Ed), 1994.

2. Peebles Jr., ‘Probability, Random Variables and Random Signal Principles’ McGraw-Hill Publishers.1987.

3. H.M. Taylor and S.Karlia ‘An Introduction to Stochastic Modeling’, Academic Press, Inc., 1984.

4. U.N.Bhat, ‘Elements of Applied Stochastic Processes’, John Wiley, New York, 1984.

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