you can use MGFs but you won't recognize the density.
Note that a cannot be zero but it can be negative.
Thanks to Mr Fantastic, I got the linear transformation of a simple exponential distribution. Now I'm trying to obtain the pdf of . It looks cumbersome, is there any simpler methods? Where follows this Gamma distribution:
It's just calculus one
I'm sure it's in your probability book, look for change of variables
You use the CDFs and then differentiate to obtain the relationship between the densities
see Dependent variables and change of variables
It's trivial to prove........
Now differentiate wrt y, the variable. Y is the RV.