ABSTRACT
This chapter discusses the several models related to the well-known Gaussian distribution, the general category of exponential distributions, and the fundamental concept of statistical sufficiency on obtaining the properties of θ. The Gaussian distribution plays an important role in parametric statistics due to the relatively simple Gaussian model and its broad spectrum of applications. Indeed, in engineering and science, the Gaussian distribution is probably the most jointly used distribution for random measurements. When a sequence of independent and identically distributed (IID) Gaussian random variables (RVs) passes through a linear filter, the output remains Gaussian distributed but is no longer IID. The filter smooths the input and introduces a correlation between the values of the input vector. One of the most useful statistical tools is the central limit theorem (CLT). The CLT allows for the approximation of the sum of the IID of the finite RVs with the use of the Gaussian distribution.
