At the beginning we recall basic facts about the well-known linear regression problem in a fixed and a random design. It is indicated that the random design problem conditioned on the independent variate (the covariate) can be regarded as a fixed design problem. Afterwards the considerations are merely based on the conditional statistical model. In contrary to the foregoing models we deal with parametric models such as the EV model. Based on a conditional maximum likelihood estimator one obtains estimators and predictions of conditional functional parameters. The required modifications for gP distributions are deduced within a Poisson process framework. Applications in environmental statistics and statistical finance are indicated.