Let X ~ exp(1), Y=e-X and consider the simple linear model , where .
Demonstrate that 1, X, X2 are linearly independent in L2.
It also gives a hint: exp(1) = G(1), (gamma distribution with p=1)
I'm not sure how to show linear independence in L2 , I'm not even quite sure what L2 means exactly. Would showing Cov(1,X) = Cov(X,X^2) = Cov(1,X^2) = 0 be enough for linear independence? I'm also no sure how to use the hint..