Random Variable & Random Process: Problem Solving Techniques

In this course, you will learn step by step procedure to solve questions on Random variables and Random process. I will discuss the problems on probability density function, cumulative probability distribution function, conditional probability, joint probability, Bayes rule, Statistical averages such as mean, mean square value, power spectral density, auto correlation, cross correlation, Uniform distribution, Gaussian random variable, Transmission of a Random process through a linear filter, properties of autocorrelation function, properties of power spectral density.

Random signals are encountered in every practical communication system. Some examples of Random signals are voice signals, television signals, digital computer data and electrical noise. A signal is random, if it is not possible to predict the exact value of the signal in advance where as a signal is deterministic, if it is possible to predict the exact value of the signal in advance. Although it is not possible to predict the precise value of a random signal in advance, it may be described in terms of its statistical properties such as the average power in the random signal. The mathematical discipline that deals with the statistical characterization of random signals is probability theory. Random signal is also called as Random process or stochastic process.

A Random variable is obtained by observing a Random process at a fixed instance of time.