Let X and W be independent and uniformly distributed on [−1,1] . We have given the following facts:

E[X]=E[X3]=E[X5]=0

E[X2]=1/3

E[X4]=1/5

Suppose that

Y=X3+W

1.Find the LLMS estimate for Y , given that X=x . (Your answer should be a function of x .)