~X 0 < x < 6 Q4/ Let X; Xz and Xz be iid with common pdf f(x) = {o e.W Xz and let Y; Yz = Ya = Ei-1X; prove that Y;,Yz, Yz are 2-1Xi 2_1* mutually independent_
Added by Cesar B.
Step 1
Since Y = (X1 + X2 + X3)/3, we can use the convolution formula to find its pdf: fY(y) = ∫∫fX1X2X3(x1,x2,x3) δ(y - (x1+x2+x3)/3) dx1 dx2 dx3 where fX1X2X3(x1,x2,x3) = f(x1)f(x2)f(x3) since X1, X2, and X3 are independent and identically distributed. Using the Show more…
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