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發問:
A population consists of the 4 numbers 2, 4, 7, 9.a) Find the population variance.b) If random samples of size 2 are drawn without replacement from this population and order is not counted, there are only 6 possible samples. Find the variance of the sample means of these 6 samples.Show your steps.(Ans.: a.... 顯示更多 A population consists of the 4 numbers 2, 4, 7, 9. a) Find the population variance. b) If random samples of size 2 are drawn without replacement from this population and order is not counted, there are only 6 possible samples. Find the variance of the sample means of these 6 samples. Show your steps. (Ans.: a. Var(X) = 7.25; b. Variance of sample means = 2.4167) 更新: To myisland8132: Thanks for your reply. But I wonder how do you come up with the expression in part b)? May you elaborate on that a bit more? thx =) 更新 2: Btw, anyone can help?
最佳解答:
(a) E(X) = (2 + 4 + 7 + 9)/4 = 5.5 E(X^2) = (4 + 16 + 49 + 81)/4 = 37.5 Var(X) = 37.5 - (5.5)^2 = 7.25 (b) Var(X_bar) =(4 - 2)/(4 - 1) * 7.25/2 = 24167 2011-11-27 21:00:50 補充： It is a formula which can be found out in any textbook of sampling theory
其他解答:
Part (b) Sample Sample Mean 2, 4 3 2, 7 4.5 2, 9 5.5 4,7 5.5 4,9 6.5 7,9 8 mean of sample mean, E(X) = 33/6 = 5.5 Sample variance = [(3^2 + 4.5^2 + 5.5^2 + 5.5^2 + 6.5^2 + 8^2) - 6 x 5.5^2]/6 = (196 - 181.5)/6 = 2.416666 = 2.4167.|||||幫你係雅虎search過，唔知道以下網址幫不幫到您，應該有您想要的東西http://hk.search.yahoo.com/search;_ylt=Axt7wJ_GPHxOIkAAIEuzygt.?p=%E5%85%A8%E7%90%83%E6%9C%8D%E9%A3%BE%E6%89%B9%E7%99%BC%E7%B6%B2-%E6%B8%AF%E8%B2%A8%E5%BB%A0%E5%AE%B6%E6%89%B9%E7%99%BC%E8%B2%A8%E6%BA%90%EF%BC%8C%E6%99%82%E8%A3%9D%E6%89%B9%E7%99%BC%E8%B2%A8%E6%BA%90&fr2=sb-top&fr=FP-tab-web-t&rd=r1 記住俾分我牙!
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Sampling Distribution發問:
A population consists of the 4 numbers 2, 4, 7, 9.a) Find the population variance.b) If random samples of size 2 are drawn without replacement from this population and order is not counted, there are only 6 possible samples. Find the variance of the sample means of these 6 samples.Show your steps.(Ans.: a.... 顯示更多 A population consists of the 4 numbers 2, 4, 7, 9. a) Find the population variance. b) If random samples of size 2 are drawn without replacement from this population and order is not counted, there are only 6 possible samples. Find the variance of the sample means of these 6 samples. Show your steps. (Ans.: a. Var(X) = 7.25; b. Variance of sample means = 2.4167) 更新: To myisland8132: Thanks for your reply. But I wonder how do you come up with the expression in part b)? May you elaborate on that a bit more? thx =) 更新 2: Btw, anyone can help?
最佳解答:
(a) E(X) = (2 + 4 + 7 + 9)/4 = 5.5 E(X^2) = (4 + 16 + 49 + 81)/4 = 37.5 Var(X) = 37.5 - (5.5)^2 = 7.25 (b) Var(X_bar) =(4 - 2)/(4 - 1) * 7.25/2 = 24167 2011-11-27 21:00:50 補充： It is a formula which can be found out in any textbook of sampling theory
其他解答:
Part (b) Sample Sample Mean 2, 4 3 2, 7 4.5 2, 9 5.5 4,7 5.5 4,9 6.5 7,9 8 mean of sample mean, E(X) = 33/6 = 5.5 Sample variance = [(3^2 + 4.5^2 + 5.5^2 + 5.5^2 + 6.5^2 + 8^2) - 6 x 5.5^2]/6 = (196 - 181.5)/6 = 2.416666 = 2.4167.|||||幫你係雅虎search過，唔知道以下網址幫不幫到您，應該有您想要的東西http://hk.search.yahoo.com/search;_ylt=Axt7wJ_GPHxOIkAAIEuzygt.?p=%E5%85%A8%E7%90%83%E6%9C%8D%E9%A3%BE%E6%89%B9%E7%99%BC%E7%B6%B2-%E6%B8%AF%E8%B2%A8%E5%BB%A0%E5%AE%B6%E6%89%B9%E7%99%BC%E8%B2%A8%E6%BA%90%EF%BC%8C%E6%99%82%E8%A3%9D%E6%89%B9%E7%99%BC%E8%B2%A8%E6%BA%90&fr2=sb-top&fr=FP-tab-web-t&rd=r1 記住俾分我牙!
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