Expectation - A Fuzzy Term in Metrology?

Within the metrology community we find several ideas concerning the importance and definition of the term "expectation". Sometimes it is used inadequately. Here we quote the most popular ones and derive, from the point of view of signal and system theory as well as of stochastics and statistics, one pair of definitions as being the most reasonable. Several familiar examples will support this systematic approach. In the surroundings of the ISO Guide to the Expression of Uncertainty in Measurement (GUM) at least the use of the term expectation is not always clear.