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Topic 9: The Law of Large Numbers
... Var( Sn ) = 2 (Var(X1 ) + Var(X2 ) + · · · + Var(Xn )) = 2 (σ + σ + · · · + σ) = 2 nσ = σ 2 . n n n n n So the mean of these running averages remains at µ but the variance is inversely proportional to the number of terms in the sum. The result is the law of large numbers: For a sequence of random va ...
... Var( Sn ) = 2 (Var(X1 ) + Var(X2 ) + · · · + Var(Xn )) = 2 (σ + σ + · · · + σ) = 2 nσ = σ 2 . n n n n n So the mean of these running averages remains at µ but the variance is inversely proportional to the number of terms in the sum. The result is the law of large numbers: For a sequence of random va ...
Interval Estimation II
... iii) Does the population have to be normally distributed here for the interval to be valid? Explain. [2 Marks] iv) Explain why an observed value of 320 hours is not unusual, even though it is outside the 95% confidence interval you have calculated. [2 Marks] ...
... iii) Does the population have to be normally distributed here for the interval to be valid? Explain. [2 Marks] iv) Explain why an observed value of 320 hours is not unusual, even though it is outside the 95% confidence interval you have calculated. [2 Marks] ...
ANOVA
... If the population means are the same, then this statistic should be close to 1. If the population means are different then between group variation (MSTr) should exceed within group variation (MSE), producing an F statistic greater than 1. ...
... If the population means are the same, then this statistic should be close to 1. If the population means are different then between group variation (MSTr) should exceed within group variation (MSE), producing an F statistic greater than 1. ...
Method of Moments - University of Arizona Math
... Method of moments estimation is based solely on the law of large numbers, which we repeat here: Let M1 , M2 , . . . be independent random variables having a common distribution possessing a mean µM . Then the sample means converge to the distributional mean as the number of observations increase. n ...
... Method of moments estimation is based solely on the law of large numbers, which we repeat here: Let M1 , M2 , . . . be independent random variables having a common distribution possessing a mean µM . Then the sample means converge to the distributional mean as the number of observations increase. n ...
1 Inference for the difference between two population means µ1 − µ2
... people being treated with one or the other drug. This would call for a method using the information in the two samples and estimating and testing properties for the two means. The sample data will give us: sample size mean s.d. ...
... people being treated with one or the other drug. This would call for a method using the information in the two samples and estimating and testing properties for the two means. The sample data will give us: sample size mean s.d. ...