Given X1,X2X_1, X_2X1,X2 are i.i.d. Uniform(0,1)Uniform(0, 1)Uniform(0,1), what is the PDF of W=X1+X2W = X_1 + X_2W=X1+X2?
fW(w)=wf_W(w) = wfW(w)=w for 0≤w≤10 \le w \le 10≤w≤1 and 2−w2-w2−w for 1<w≤21 < w \le 21<w≤2
fW(w)=1f_W(w) = 1fW(w)=1 for 0≤w≤10 \le w \le 10≤w≤1
fW(w)=w2/2f_W(w) = w^2/2fW(w)=w2/2
fW(w)=1/2f_W(w) = 1/2fW(w)=1/2