ABSTRACT
Most engineering systems are subject to noise. Noise variables are considered random functions of time and are characterized by their average properties and probability distribution functions. This chapter considers two random experiments, performed simultaneously, both with a finite number of outcomes. It focuses on the behavior of discrete linear dynamic systems will be investigated when subjected to random inputs. However, it is possible to define the relative frequency, and thus the probability, of the variable being smaller than a particular value. The bivariate density function, if it arises from a smooth distribution, can also be considered as a local measure of probability. A problem involving composite hypotheses may be reduced to testing simple hypotheses by the following idea. Hypothesis testing is one of the central subjects of mathematical statistics. Intuition suggests to seek the parameter estimates as the parameter values with which the distribution assigns the highest local probability to the actual observations.
