## Probability distributions, Random Processes and Numerical Methods

**MODULE I**

- Discrete random variables, probability mass function, cumulative distribution function, expected value, mean and variance.
- Binomial random variable-, mean, variance.
- Poisson random variable, mean, variance
- approximation of binomial by Poisson. Distribution fitting-binomial and Poisson

**MODULE II**

- Continuous random variables
- Probability density function, expected value, mean and variance.
- Uniform random variable-, mean, variance.
- Exponential random variable-mean, variance, memoryless property.
- Normal random variable-Properties of Normal curve mean, variance (without proof), Use of Normal tables.

**MODULE III**

- Joint probability distributions- discrete and continuous, marginal distributions, independent random variables.(More Examples)
- Expectation involving two or more random variables, covariance of pairs of random variables. Central limit theorem (without proof).

**MODULE IV**

- Random processes, types of random processes, Mean, correlation and covariance functions of random processes, Wide Sense Stationary (WSS) process ,Properties of autocorrelation and auto covariance functions of WSS processes. – (Lecture 2)
- Power spectral density and its properties

**MODULE V**

- Poisson process-properties, probability distribution of inter arrival times. ( Lecture 2)
- Discrete time Markov chain- Transition probability matrix, Chapman Kolmogorov theorem (without proof),
- computation of probability distribution and higher order transition probabilities, stationary distribution

**MODULE VI**

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