有3題統計問題 請會的人可以提點一下 打的不是很好 請見諒 謝謝 1.This exercise shows that the sample variance is an unbiased estimator of the population variance when Y1…..Yn ﹐are i.i.d with meanμ(y) and varianceσ^2 (y) . _ 2 _ _ a. show that E[(Yi-Y)] = Var(Yi) +2cov(Yi,Y) +Var(Y) _ b. show cov(Yi,Y )= σ^2 (y)/n 2 2 c. use the results in parts (a) and (b) to show E(S(y))= σ (y) 2. Suppose that (Xi,Yi) are i.i.d with finite forth moments. Prove that the sample covariance is a consist estimator of the population covariance that is Sxy =σxy 3. _ _ show that the pooled standard error {SE(pooled)[Y1-Y2]} equals the stardend error for the difference in means when the two group sizes are the same. -- t a ╭◥███◣══╮ ◥██ █◤ ╭══════theanswer3╮ h n ║ █▌ █ ● ╰══════╯█▌ █╰══╯● ◣ ║ e s ║ █▄▄◤ ◢ ◢█◣ . █▌ █ ◢█◣ ◢ ◥█◣ ☆╴D ║ w ║ █▄▄◣ █ █▌█.‵﹑ ˙ █▌ █ █▌█ █ █ ︻ ▄ ║ e ║ █▌ █ ◤ ◥██∵ ￠☆ ────────────── ﹀ ╭▄﹀ r 3╰◢███◤═══▄◤═〞′══◥██◤═══════════════╯ --

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