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109年 - 109中原大學_碩士班招生考試_工業與系統工程學系甲組︰機率與統計#101455
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4. A random samples of 64 observations produced with the sample mean of 0.323 and the sample variance of 0.034. Test the hypothesis that if the population mean is less than 0.36 using the significance level of 0.10.
相關申論題
1. Calculate the mean and standard deviation for the following sample: 0, 2, 0, 0, -1, 1, -2, 1, 0, -1, 1, -1, 0, -3, -2, -1, 0, 1
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(a) Calculate the standard deviation of sample mean.
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(b) If P (sample mean > 19.1) = .5, what is the population mean?
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3. A random sample of 75 measurements was selected from a population with the variance of 12. The sample mean is 28. Calculate a 95% confidence interval for the population mean.
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b. [8%] Find the Cramer-Rao lower bound for the variance of any unbiased estimate of θ.
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a. [8%] Find sufficient statistics for θ.
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7. [10%] Suppose that a vector a consists of two random variables as x = (X1, X2)T, whose 2 x 2 variance-covariance matrix is Let w = (w1, w2)T be a given vector of known weights. Prove that the variance of the random variable
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b. [7%] Find the maximum likelihood estimator for a.
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a. [7%] Find a method of moments estimator for a in terms of the sample mean.
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5. [16%] Fill in the cells ⓐ~ⓔ on the incomplete analysis of variance table below from a one way randomized design. Also write down ⓕ the null hypothesis, ⓔthe alternative hypothesis, and ⓗ the conclusion for the F test using a significance level of 5%.
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相關試卷
110年 - 110 國立中山大學碩士暨碩士專班招生考試_應數系碩士班/甲組:機率與統計#105484
110年 · #105484
109年 - 109中原大學_碩士班招生考試_工業與系統工程學系甲組︰機率與統計#101455
109年 · #101455