KTU B.Tech S4 Lecture Notes on MA204 Probability distributions, Random Processes and Numerical Methods
- 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
- 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.
- 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).
- 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
- 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
- Finding roots of equations-Newton-Raphson method. Interpolation-Newton’s forward and backward difference formula, Lagrange’s interpolation method. Numerical Integration-trapezoidal rule, Simpson’s 1/3rd rule. Numerical solution of first order ODE-Euler method, RungeKutta fourth order (classical method).