Convolution of two functions (pdfs)

Question

I want to convolve two signals . The range of each of the signal is 0 to 1.

                             y1={1/(y1)0.5} -1
                             y2={1/(y2)0.5} -1
                             z=y1+y2

I want to convolve the above two signals.Basically the above two are pdfs.I want to find the pdf of the sum of the above two pdfs.So, I need to convolve the above two pdfs.

I want to know what should be the range for the convolution in my case.Secondly,Convolving above two will result some terms in Z.Am I doing right.Please help me out as I am weak in convolution.