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## Main Question or Discussion Point

Suppose X and Y are Uniform(-1, 1) such that X and Y are independent and identically distributed. What is the density of Z = X + Y?

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

f

The density of Z will be given by

f

f

So,

f

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

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 otherwiseThe density of Z will be given by

f

_{Z}= [tex]\int[/tex]f_{X}(z-y)f_{Y}(y)dyf

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

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