# What is the relationship between probability densities and mass densities?

In statistics we have probability distribution functions which give us likelihood that some random variable ($$X$$) will equal a particular value. Assuming this variable is continuous, the distribution satisfies: $$\int f_{X}(x) \ dx = 1$$

and can be used to obtain the moments of the variable \begin{align} \mu'_i = \int X^i f_x(x) dx \end{align}

In physics we often work with the mass distribution function which describes the distribution of mass. For example the total mass across a system is given by: $$M_{tot} = \int g_M(m) \ dm$$

and like the statistical PDF we can also derive moments of this mass distribution function by integrating across the distribution function: $$\mu'_i = \int m g_M(m) \ dm$$

I am wondering what the connection between these two concepts is and if there is any way to move between them?