... 172 ] Briefly, the count rate at the detector from a source at a redshift z is . ... Figure 55 shows the ``Green functions'' for the double compact binary merging rate   evolution assuming no collapse anisotropy. ... Another way that diverse peculiarities in the - distribution induced by the sources evolution could arise is connected with a possible non-monotonic character of the star formation rate in galaxies. ... 22 ] Figure  56 shows two-dimensional cuts through the parameter space. ...

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... Where we have just a single image we assume a probabilistic mode of source detection such that, at a given image pixel, if the probability that the observed value at that pixel could have arisen through statistical fluctuation of the background at that pixel lies below a certain limiting probability , the pixel is considered to contain a source. In XMM practice it is likelihood rather than itself which is employed; in this case the detection criterion is for to exceed the cutoff . ...

... Using the central limit theorem, the total noise can be approximated by a Gaussian or normal distribution which has the frequency function : . ... where is the mean intensity of the source. ... In the statistical analysis of the probability distribution of data several estimators based on moments are used. ... For a normal distribution, these moments are and while for a Poisson distribution are and . Besides these moments other estimators are used to describe a distribution e.g. median and mode . ...