- #1
Shannon Young
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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
fX(x) = fY(x) = 1/2 if -1<x<1 and 0 otherwise
The density of Z will be given by
fZ= [tex]\int[/tex]fX(z-y)fY(y)dy
fY(y) = 1/2 if -1<y<1 and 0 otherwise
So,
fZ= [tex]\int[/tex](1/2)fX(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
Here is what I have done so far (I am new to this forum, so, my formatting is very bad). I know that
fX(x) = fY(x) = 1/2 if -1<x<1 and 0 otherwise
The density of Z will be given by
fZ= [tex]\int[/tex]fX(z-y)fY(y)dy
fY(y) = 1/2 if -1<y<1 and 0 otherwise
So,
fZ= [tex]\int[/tex](1/2)fX(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