This book presents the author’s new method of two-stage maximization of a likelihood function, which helps to solve a series of non-solving before the well-posed and ill-posed problems of pseudosolution computing systems of linear algebraic equations (or, in statistical terminology, parameters’ estimators of functional relationships) and linear integral equations in the presence of deterministic and random errors in the initial data. This book presents, for the first time, a solution of the problem of reciprocal influence of passive errors of regressors and of active errors of predictors by computing point estimators of functional relationships.