Let X~exp(1), Y=e-X and consider the simple linear model Y= \alpha + \beta X + \gamma X^2 + W with  E(W) = 0 = \rho(X, W) = \rho(X^2, W)

I need to evaluate the constants alpha, beta, and gamma using the information given above. I'm wondering if I am doing this correctly. I showed that Y~unif(0,1) which made calculations a bit easier, then I found E(Y), Cov(X,Y), Cov(X2,Y), got 3 equations and solved for the 3 unknowns.


pic of my work:http://i.imgur.com/HHlMl.jpg
moment calculations:http://i.imgur.com/O0m0h.jpg


I can't figure out where I went wrong; the next part of the question involves calculating sigma(W)/sigma(Y), and using my calculated coefficients I am getting a negative number for sigma(W).
Can someone point out where I'm making a mistake and/or how to do part c?