Q and A Bank 2.10 (i)

[mcallist]

Hi there,

Can someone please explain the following algebra.

In the solution, to part (i), when getting the updated the estimate for E(s^2(theta)), there's one part where the last two terms are added together to simplify the expression. Please if someone could explain, that would be great. Please see the picture attached.

Thanks a lot,
Tom

 

[John Lee]

I'm confused - are you just asking how \(-2\bar X_I \sum\limits_{j=1}^{10} P_{Ij} X_{Ij} +\bar X_I^2 \sum\limits_{j=1}^{10} P_{Ij}\) becomes \(-\bar X_I^2 \sum\limits_{j=1}^{10} P_{Ij}\)?

In which case, all that has happened is they have rearranged the given result to \(\sum\limits_{j=1}^{10} P_{Ij} X_{Ij} = \bar X_I \sum\limits_{j=1}^{10} P_{Ij}\) and substituted it in.

 

[mcallist]

That's great, thanks John