| 1. |
Sampling and resampling methods have become more useful in recent years
due to the power of computers. Define "sampling" and "resampling" methods
as well as discuss their applications. (15%) |
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| 2. |
(1) What is a parametric statistical method? Name and describe some
parametric methods you have used. (6%) |
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(2) What is a nonparametric statistical method? Name and describe some
nonparametric methods you have used corresponding to your answer in (1).
(6%) |
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(3) List the advantages and/or disadvantages of nonparametric testing
compared with parametric methods. How serious are these shortcomings?
(6%) |
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| 3. |
有一個礦工身陷在有三個分叉隧道的礦洞中，若選擇第一個隧道，則礦工將花費兩小時安全的離開礦洞；若選擇第二個隧道，則礦工將花費三小時，並重回此三叉口；若選擇第三個隧道，則礦工將花費五小時，並重回此三叉口。假設礦工選擇各個隧道的機率相同，則礦工安全離開礦洞的期望時間為多少？（請說明你的解題概念與過程）
(15%) |
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| 4. |
(1)若x是一個隨機變數，且為正數，若a> 0，則證明：（馬可夫不等式） |
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(6%)  |
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(2)若x是一個隨機變數，其平均數為u，變異數為σ2，若k > 0，則證明：（切氏不等式） |
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(6%)  |
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(3)請說明馬可夫不等式與切氏不等式的功用與重要性。 (6%) |
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| 5. |
請列舉四種在商學、企管領域，探討兩個變數間關係的統計或計量方法，並詳細比較各個方法間在 |
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| (1) |
變數資料內涵﹝屬質(qualitative)或屬量(quantitative)，時間序列(time series)或橫斷面(cross
sectional)﹞，及 |
| (2) |
分析產生結果內涵（即分析後所呈現的訊息）上的差別。 (14%) |
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| 6. |
請列舉四種在商學、企管領域，探討三個以上變數間關係的統計或計量方法，並詳細比較各個方法間在 |
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| (1) |
應變數及自變數的個數， |
| (2) |
變數資料內涵﹝屬質(qualitative)或屬量(quantitative) ，時間序列(time series)或橫斷面(cross
sectional)﹞，及 |
| (3) |
分析產生結果內涵（即分析後所呈現的訊息）上的差別。 (20%) |
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