Chapter 9 - Var (s^2)

Top of page 9 using Chi^2 to work out E(S^2) and Var (S^2):
I'm using 0 to represent sigma.

Var [(n-1)S^2/0^2] = 2(n-1). Therefore Var(S^2) = 0^4/(n-1)^2 *2(n-1).

Why is 0 raised to 4 (not 2) and why is (n-1) ^2 rather than just (n-1)?

In other words why has this equation been multiplied by an extra sigma^2/(n-1)?

Is it because it is the second moment? Could you refer me back to the page in the notes which would help me with this please.

Cheers

 

It is because the coefficient has to be squared. Remember var (aX) = a^2 var (X).

 

Thanks Freddie. Sometimes its the simple stuff that gets overlooked. Getting stressed!