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題組內容

2. Let X₁,...., X_n be a random sample from the following density function

(a) (5 points) Find the MLE (maximum likelihood estimator) of 6. Is it an unbiased estimator?

相關申論題

(b) (10 points) Use the MLE in (a) to obtain a 100 x (1 - c)% confidence interval for θ. Hint: is distributed as a Chi-square distribution.

(a) (5 points) Find the method of moment estimator of θ.

(b) (10 points) Find the limiting distribution of as n→∞ by the Delta method, where Tis the method of moment estimator of θ.

(a) (5 points) Find the uniform minimum variance unbiased estimator (UMVUE) of g(μ).

(b) (5 points) Find the Cramer-Rao lower bound (CRLB) for the variance of unbiased estimator of g (μ). Is the CRLB attained by the variance of the UMVUE?

(a) (2 points) When significant level is set as 0.05, fine the rejection region of X.

(b) (2 points) When X, reject H0. Find the probability of type I error.

(c) (2 points) When X , reject H0. Find the probability of typeerror.

(d) (2 points) When , reject H0. Find the power of the test.

(e) (2 points) When hypothesis test: with the same significant level a given in Question(a), find the rejection region.

相關試卷

110年 - 110 國立臺灣大學_碩士班招生考試_農藝研究所生物統計學甲組:統計理論#102885

110年 · #102885

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