Kinetic theory - Maxwell-Boltzmann Distribution

[realitybugll]

My (first) question is - is a Maxwell-Boltzmann distribution function a "cumulative distribution function."?

 

[alxm]

The Maxwell-Boltzmann distribution is a continuous probability distribution of continuous variables, so it has both a probability density function and a cumulative distribution function where the latter is just an integral over the former.

 

[realitybugll]

Ah, ok. I appreciate your reply.

I guess I'm wondering then why the Maxwell-Boltzmann distribution doesn't just take the general form of the cumulative distribution function (the derivative of which is the probability mass function) with appropriate constants.

Here are pictures of the equations of each -

probability mass function:
http://upload.wikimedia.org/math/0/c/1/0c1ae7a35c20afa9f189dffa5d3c0c23.png

cumulative distribution function:
http://upload.wikimedia.org/math/3/3/4/334f6d225a50d1e4777b8e7915215577.png

both are located in the binomial distribution article -
http://en.wikipedia.org/wiki/Binomial_distribution

I don't follow any derivations of the maxwell-boltzmann distribution I've found (I probably should work harder to understand), and when I tried to derive it myself I got the cumulative distribution function. The problem with this is (a) it's somehow different than the maxwell-boltzmann distribution, and (b) I have no idea how to evaluate it.