Here is the derivation on dsplog:
http://www.dsplog.com/2008/07/17/derive-pdf-rayleigh-random-variable/
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The mode of the Pareto distribution is its lowest value.
ref veeru
The Gaussian distribution is the same as the normal distribution. Sometimes, "Gaussian" is used as in "Gaussian noise" and "Gaussian process." See related links, Interesting that Gauss did not first derive this distribution. That honor goes to de Moivre in 1773.
Easy. The mean deviation about the mean, for any distribution, MUST be 0.
I derive that this question needs to be moved.