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110年 - 110 國立中山大學_碩士暨碩士專班招生考試_經濟所:統計學#104423

科目：研究所、轉學考(插大)◆統計學 | 年份：110年 | 選擇題數：0 | 申論題數：5

試卷資訊

所屬科目：研究所、轉學考(插大)◆統計學

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申論題 (5)

1. (20%) Suppose X and Y are jointly distributed according to the joint pdf
61ad6ae741ddd.jpg
2. (20%) If the random variable X has a Poisson distribution such that P(X 1) = P(X=2). Find P(X =4).

3. (20%) Find the method-of-moments estimates for pu and σ2 based on a random sample of size n taken from an N(u,o?) distribution.

4. (20%) A random sample of size 2 is drawn from a uniform pdf defined over the interval [0,θ]. We wish to test
  61ad6b8ae05ea.jpg
 by rejecting H0 when y1 + y2≤k. Find the value for k that gives a level of significance of 0.05.
5. (20%) Let x = (X1, X2, X3)' have a trivariate normal distribution with means 6, 4, and 2 and variance 16, 25, and 64, and with cou(X1, X2) = 6 and coc(X1,X3) = 4 and cou(X2,X3)=5. Let Y1=2X1+3X2+ X3 +2 and Y2 =4X1+ X3 +3. What is the joint distribution of y = (Y1, Y2)'?