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In this paper we investigate some basic properties of the multi-modelensemble systems, which can be deduced from a general characteristic ofstatistical distributions of the ensemble members with the help ofmathematical tools. In particular we show how to find optimal linearcombination of model results, which minimizes the mean square error both inthe case of uncorrelated and correlated models. By proving basic estimationswe try to deduce general properties describing multi-model ensemble systems.We show also how mathematical formalism can be used for investigation of thecharacteristics of such systems

&lt;i&gt;Est modus in rebus&lt;/i&gt;: analytical properties of multi-model ensembles

<i>Est modus in rebus</i>: analytical properties of multi-model ensembles