# Joint probability distributions of variables satisfying a certain constraints

Here is my question:

Given a set of random variables - $\{x_i\}, i=1,2, \dots, n$, and the corresponding pdfs are given by $\{PDF_i\}, i=1,2, \dots, n$.

Now if I were it impose a certain set of constraints on random variables as following

$\{f_1(x_1,x_2, ... x_n)=C_1, f_2(x_1,x_2, ... x_n)=C_2, \dots, f_m(x_1,x_2, ... x_n)=C_m\}$

what will be the joint probability distribution - $PDF(x_1,x_2, ... x_m)=\;?$

Here is an example: The above problem was a generalization of the problems, deriving pdfs in statistical physics, like Maxwell-Boltzmann distribution of ideal gas velocity with a constraint that energy of the system is constant.

• One needs the question to be much more specific before being able to say anything valuable about it. Surely you have a specific setting in mind, let me suggest you explain this setting.
– Did
Nov 23, 2013 at 16:00
• This was a generalization of the problem I am looking for. A simple example would be deriving pdfs like maxwell-blotzmann distribution of velocity by adding a constraint that energy is constant. Nov 25, 2013 at 1:48
• Then "let me suggest you explain this setting" in details in the question.
– Did
Nov 25, 2013 at 7:52