TABLE OF CONTENTS In this section we shall consider a derivation of MLEs for some distribution families that appear in applications. As it was already mentioned, when constructing the MLEs, we shall employ the MLEs constructed previously (see e.g. Johnson et al. (1994), (1995)). As above, the estimators are based on the samples 
, and 
(see (2.2)), where n 1= n 2= n if X and Y are dependent variables. Since the volume of this book does not allow to discuss construction of the MLEs for every distribution family satisfying the above criterion, we shall elaborate derivation of the MLEs only for a number of distributions leaving the rest for exercises. We shall begin with the normal distribution which dominated statistical practice for over 100 years.
Let X and Y be independent normal variables with the means ? 1, ? 2 and variances 
and 
, respectively. In this subsection and subsection 3.2.1 we shall consider independent X and Y only. In the situation when X and Y are dependent normal variables, they can be viewed as a two-dimensional random vector X= (X, Y) and estimation of P(X
If X and Y are independent, then Y ?
