作者reluctant (生命就是燃燒)
看板NTU-Exam
標題[試題] 98上 張勝凱 計量方法入門 期末考
時間Sat Sep 12 22:00:42 2009
課程名稱︰計量方法入門
課程性質︰必修
課程教師︰張勝凱
開課學院：社會科學院
開課系所︰經濟研究所
考試日期（年月日）︰98年9月11日
考試時限（分鐘）：100
是否需發放獎勵金：是
（如未明確表示，則不予發放）
試題 :
Problem 1. True of False (25 points (5,5,5,5,5))
1. If yi = xi'β + εi, xi is an element of R and E(εi|xi) = 0,
then εi is independent of xi.
2. If yi = xi'β + εi, xi is an element of R and E(εi|xi) = 0,
then E(xi^2εi) = 0.
3. If yi = xi'β + εi, xi is an element of R and E(xiεi) = 0,
then E(xi^2εi) = 0.
4. If Y is uncorrelated with E(Y|X), then Y is uncorrelated with X.
5. If Y is mean independence of X, then Y^2 is mean independence of X.
Problem 2.(25 points (5, 10, 10))
Let θcap = (θ1cap, θ2cap)' be a N square-root- asymptotically normal
estimator for θ = (θ1, θ2)'.
Let γcap = 2θ1capθ2cap be an estimator of γ = 2θ1θ2.
1. Is γcap a consistent estimator of γ? Explain.
2. Find Avar(γcap) in terms of θ and Avar(θcap).
3. If, for a sample of data, θcap = (1,2)' and Avar(θcap) is estimated as
[1 -0.5 ]
[-0.5 2 ]
find the asymptotic standard error of γcap.
Problem 3.(25 points (5,10,10))
Let the joint pdf by
f(x,y) = 6xy^2 , 0 < x < 1, 0 < y < 1.
= 0 , elsewhere
(1) Verify f(x,y) is a legitimate joint pdf function.
(2) Find E(Y|X). Is Y mean independent of X ?
(3) Find BLP of Y given X. Is Y uncorrelated with X ?
Problem 4.(25 points (15,10))
(a) Let Xi, i = 1,2,.... be an independent Berboulli(p) random variables and
let Yn = ΣXi / n. Then, find the asymptotic distribution of Yn/(1-Yn).
(b) Let X1, ..., Xn be a random sample from a population with meanμ and
varianceσ^2.
Find E((Xnbar - μ)n^0.5/2σ) and Var((Xnbar - μ)n^0.5/2σ).
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◆ From: 123.193.251.73
※ 編輯: reluctant 來自: 123.193.251.73 (09/12 22:02)
1F：推 gavin79115 :98上不是還沒開始嗎@@XD 09/12 22:23
2F：推 Jackliu2619 :原po批幣缺很大喔 科科 這科的開課方式考古題應該僅 09/12 22:40
3F：→ Jackliu2619 :供參考而已吧 XD 09/12 22:40
4F：推 abacada :期前考? 09/13 15:00
5F：→ TINTINH :這個我也不知道是不是該收在經濟系 請板主指示 感謝! 09/13 16:08
6F：推 youngsam :經濟所碩一必修課 於暑假上課 09/13 22:02
7F：→ youngsam :不過每年授課老師有可能不同 09/13 22:02
8F：→ youngsam :授課內容也由授課老師決定 09/13 22:02
9F：推 abacada :看樣子是98上沒錯 只是暑假就開課這樣 09/18 22:04
10F：推 abacada :大概像一些科法所那樣吧 經研所的課 麻煩小板主囉~ 09/18 22:04
11F：推 TINTINH :已收:) 09/21 10:01
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※ 發信站: 批踢踢實業坊(ptt.cc)
◆ From: 140.112.211.45
※ 編輯: Jackliu2619 來自: 140.112.211.45 (09/09 12:20)
12F：推 Dboy:看到這個就想到我那白癡的delta method.... 09/09 13:17
13F：推 assamb:謝謝助教呵呵 09/09 15:29
14F：推 kokominana:非常謝謝JACK大熱心貢獻 不過我考完才看到.... 09/12 19:38
15F：→ Jackliu2619:沒差 反正這份考古題也只命中一題而已(8%)..... 09/12 21:47