阿摩線上測驗
登入
首頁
>
研究所、轉學考(插大)◆統計理論
>
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
> 申論題
題組內容
2. Let X
1
,...., 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
1. (10 points) Let X~Beta(a,β) and Y~Beta(a + β,γ) be two independent variables of beta distribution. Find the distribution of XY by making the transformations U=XY, V=Y. The pif of beta distribution, Beta(a,b), is given by
#434203
(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.
#434205
(a) (5 points) Find the method of moment estimator of θ.
#434206
(b) (10 points) Find the limiting distribution of as n→∞ by the Delta method, where Tis the method of moment estimator of θ.
#434207
(a) (5 points) Find the uniform minimum variance unbiased estimator (UMVUE) of g(μ).
#434208
(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?
#434209
(a) (2 points) When significant level is set as 0.05, fine the rejection region of X.
#434210
(b) (2 points) When X, reject H0. Find the probability of type I error.
#434211
(c) (2 points) When X , reject H0. Find the probability of typeerror.
#434212
(d) (2 points) When , reject H0. Find the power of the test.
#434213
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
阿摩線上測驗
登入
阿摩線上測驗
登入