- 18

- 0

## Main Question or Discussion Point

I know I already posted this but I made a mistake in the original post which I realized now and I am reposting the correct problem as i am not able to edit it.

Given

X(i) = u + e(i) i = 1,2,...N

such that e(i)s are statistically independent and u is a parameter

mean of e(i) = 0

and variance = [tex]\sigma(i)[/tex]^2

Find W(i) such that the linear estimator

[tex]\mu[/tex] = [tex]\sum[/tex]W(i)X(i) for i = 1 to N

has

mean value of [tex]\mu[/tex]= u

and E[(u- [tex]\mu[/tex])^2 is a minimum

For a linear estimator:

W(i) = R[tex]^{}-1[/tex]b

where b(i)= E([tex]\mu[/tex](i) X(i)) and R(i) = E(X(i)X(j))

I do not know how to proceed beyond this. Thanks for your help

**1. Homework Statement**Given

X(i) = u + e(i) i = 1,2,...N

such that e(i)s are statistically independent and u is a parameter

mean of e(i) = 0

and variance = [tex]\sigma(i)[/tex]^2

Find W(i) such that the linear estimator

[tex]\mu[/tex] = [tex]\sum[/tex]W(i)X(i) for i = 1 to N

has

mean value of [tex]\mu[/tex]= u

and E[(u- [tex]\mu[/tex])^2 is a minimum

**3. The Attempt at a Solution**For a linear estimator:

W(i) = R[tex]^{}-1[/tex]b

where b(i)= E([tex]\mu[/tex](i) X(i)) and R(i) = E(X(i)X(j))

I do not know how to proceed beyond this. Thanks for your help