# MA8451 – Probability and Random Processes – Regulation 2017 Syllabus

## MA8451 – SYLLABUS

### UNIT I PROBABILITY AND RANDOM VARIABLES

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

Joint 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

Classification — Stationary process — Markov process — Markov chain — Poisson process — Random telegraph process.

### UNIT IV CORRELATION AND SPECTRAL DENSITIES

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

### UNIT V LINEAR SYSTEMS WITH RANDOM INPUTS

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

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