Mei want to estimate the proportion ,P, of Hong Kong people who are not wearing mask when riding the MTR.Mei choose 100 MTR riders and count X, the number who do not wear masks.Mei's estimate for P is p=X/100.
a. Prove whether or not p is a maximum likelihood estimator
b. Prove whether or not p is an unbias estimator
statistics problem
2014-05-06 10:40 pm
回答 (2)
2014-05-08 7:54 am
✔ 最佳答案
(a) X follows Bernoulli distribution with parameter pL(x1,x2,...xn | p) = p^(Σ x_i) * (1 - p)^(n - Σ x_i)
ln L(x1,x2,...xn | p) = (Σ x_i) ln p + (n - Σ x_i) ln (1 - p)
∂ln L(x1,x2,...xn | p)/∂p = (Σ x_i)/p - (n - Σ x_i)/(1 - p)
Let ∂ln L(x1,x2,...xn | p)/∂p = 0
(Σ x_i)/p - (n - Σ x_i)/(1 - p) = 0
(Σ x_i)(1 - p) = (n - Σ x_i)p
p = Σ x_i/n
So, p is a maximum likelihood estimator
(b) E(p)
= E(Σ x_i/n)
= E(Σ x_i/100)
= [E(x_1) + E(x_2) + ... + E(x_100)]/100
= 100(x_bar)/100
= x_bar
So, p is an unbias estimator
2014-05-07 3:13 am
Yes and Yes~
可惜我忙到不得了沒時間答你～
你寫出個 likelihood function 自己 d 一次搵個 MLE 就知～
你另外果題 Neyman-Pearson Lemma 我都好想答～
但真係無時間～
好難得呢度有番ｄ advanced 一點的數學題可以交流一下～
可惜我忙到不得了沒時間答你～
你寫出個 likelihood function 自己 d 一次搵個 MLE 就知～
你另外果題 Neyman-Pearson Lemma 我都好想答～
但真係無時間～
好難得呢度有番ｄ advanced 一點的數學題可以交流一下～
收錄日期: 2021-04-24 23:19:05
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20140506000051KK00096