Let X and Y be independent random variable such that x U (0,1) and y U (0,a). Find the density function of Z= X+Y. remark: Note that there are two...

Let X and Y be independent random variable such that x  U (0,1) and y  U (0,a). Find the density function of Z= X+Y.

remark:

Note that there are two case: a>=1 and a <1

the uniform distribution U (0,1) the density function is f(x)=1