I'm learning about transformation in mathematics in general. There are many of them like for example Jacobian (which I'm trying to understand now). The "how ?" part is very easy. There are formulas and we use them but the "why ?" part is what I'm looking for. I fail to understand the intuition behind it. Why are we using transformations ? Any links, suggestions, are all welcome.
My apologies for ambiguity. Here is an example question. Let X1, X2, . . ., Xn be independent identically distributed U (0, θ) random variables. What is the distribution of (X1-X2) ?
I can solved this question directly but it is very simple to use Jacobian to solve this. I've the solution so I know how to use it. But why are we using Jacobian and how do I know when to use it ?