What is meant by jacobian transformation of r.v.s and how can I do that?If there is link of the lecture of that topic please post it.
If you have access to a library you will find shelves of books on statistics that answer this question.
And a few minutes sifting through the results of a Google search will turn up several links. I know this because I did it. And since, I suppose, it would be churlish to say this and then end the post, I will give one link: http://www.math.uiuc.edu/~r-ash/Stat/StatLec1-5.pdf. But really ..... this is surely the sort of thing you can (and should) do yourself. Often, you learn more by doing the search yourself than by being given the information on a platter.
I really like that handout.
I like to show the sum to two uniforms is that triangular density, since it uses non-traditional techniques
(neither jacobians nor MGFs).
But this also shows how to obtain the beta constant in a Beta density and how the sample mean and variance are independent in the normal setting.
The proof of the latter in many books was incorrect for years.