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Here is what I have done so far (I am new to this forum, so, my formatting is very bad). I know that

f

_{X}(x) = f

_{Y}(x) = 1/2 if -1<x<1 and 0 otherwise

The density of Z will be given by

f

_{Z}= [tex]\int[/tex]f

_{X}(z-y)f

_{Y}(y)dy

f

_{Y}(y) = 1/2 if -1<y<1 and 0 otherwise

So,

f

_{Z}= [tex]\int[/tex](1/2)f

_{X}(z-y)dy (bounds of integration -1 to 1)

The integrand = 0 if -1<z-y<1 or if z-1<y<z+1

That is where I get stuck, and need help to complete. Your assistance is appreciated, thanks