I have a function say,
f[x_,y_,z_]:=x^3+(y+z)^4
Now the parameters have their allowed ranges
x€[0,5], y€[9,12], z€[0,4]
How to find the PDF using Mathematica and also plot Histogram of f[ ] vs PDF
Your function has no unknown parameters. If you want that function to be a pdf, then that function should integrate to 1:
Integrate[(x^3 + (y + z)^4)/1584519, {x, 0, 5}, {y, 9, 12}, {z, 0, 4}]
(* 1 *)
But that assumes the values that can be taken by each variable do not depend on the other values.
For a “histogram” you would need samples from this distribution. This would result in a 4-dimensional figure. (Same thing for the PDF.)
What am I missing?