114年 - 114 國立臺北大學_碩士班一般入學考試試題_企業管理學系甲組：統計學#146907

(1) \( \beta_{1} \) 的估計滿足一致性(consistency)指的是什麼？(\( 10\% \))

(2) 不滿足這個特性對 \( \beta_{1} \) 的估計有何影響？(\( 10\% \))

(1) 這個發現對行銷人員有什麼意涵？(20%)

(2) 如果行銷人員想要得到更具體的結果，您認為接下來該進行什麼分析？(10%)

Part II

1. A group of 6 friends are exchanging Christmas gifts. In how many ways can they exchange gifts so that no one receives their own gift? (15%)

2. Given that the lifetime of a particular device follows an exponential distribution with a mean of \( x \) hours, find the expected lifetime of the device, given that it has lasted at least \( Y \) hours. (15%)

3. A rare medical condition affects only 1 in 50,000 people in a specific population. A sophisticated diagnostic test for this condition has the following characteristics:

●If a person has the disease, the test is \( 99.5\% \) accurate in detecting it (sensitivity).
●If a person does not have the disease, the test has a \( 1.5\% \) false positive rate.
●Two independent tests are performed on the same patient.

What is the probability (%) that a person actually has the disease, given that they tested positive on the first test and also tested positive on the second test? (20%)

(Note: You are asked to answer in percentages, counted to two decimal places.)