Boltzman Distribution - page 13
This condition requires C = 1/kT and the probabilty distribution becomes
The normalization constant C is characteristic of the system being described. It depends on how the energy is determined for the entities in the system and on the number of entities that can have the same energy.
For the system analyzed here, we assumed that an entity simply can possess an energy between zero and infinity and that any number of entities can have the same energy. We leave the energy expressed simply as E and perform the normalization integration:
This is a specialized form of the Boltzman probability distribution function.