W = POP- THEOREM I. If SS is the variance of a random sample from an infinite ulation with the finite variance o?, then
Posted: Wed Nov 24, 2021 9:18 am
- W Pop Theorem I If Ss Is The Variance Of A Random Sample From An Infinite Ulation With The Finite Variance O Then 1 (109.51 KiB) Viewed 90 times
W = POP- THEOREM I. If SS is the variance of a random sample from an infinite ulation with the finite variance o?, then E(S2) = . Proof By definition of sample mean and sample variance, GMA E(S) = E = (X;- 2 71 - i=1 E[y] - Σας- ] 31x- – – 1 ANTS E {(X; – 1) - X - })} i=1 E{(X; – ?) -n-E{(X – )2} n i=1 o 02 it follows that 9 = n Then, since E{(X; – )2) = 02 and E{1} – 1)?} Jag 1 = 0? 02 E(S) o-n. n n-1 i=1