On a probabilistic derivation of the basic particle statistics (Bose–Einstein, Fermi–Dirac, canonical, grand-canonical, intermediate) and related distributions

Combining intuitive probabilistic assumptions with the basic laws of classical thermodynamics, using latter to express parameters in terms thermodynamic quantities, we get a simple unified derivation fundamental ensembles statistical physics avoiding any limiting procedures, quantum hypothesis and even entropy maximization. This point view also leads some related classes correlated particle statistics.