2. 研究人員進行資料分析設立了一個線性迴歸模式：Y = β0 + β1X1 + β2X2 + , β0 - β1 - β2 是截距項與 X1 - X2 的係數，是殘差項，樣本大小 n 。該研究人員想知道不納入解釋變數 X2 對 β1 估計結果會產生什麼影響。請討論其影響為何？(20%)

4. A prestigious art gallery is hosting an exhibition of 10 sculptures. The gallery has 10 pedestals arranged in a perfect circle. Among these sculptures are three specific pieces created by the same artist (Tom), which we will label A1, A2, and A3. The other seven sculptures are created by seven different artists. The curator has dictated the following strict conditions for the installation: Condition 1: The Artist's Constraint: No two of the Tom's sculptures (A1, A2, A3) can be placed on adjacent pedestals. Condition 2: The Rotational Symmetry: Because the pedestals are in a circle and the room is perfectly uniform, two arrangements are considered identical if one can be rotated into the other. Condition 3: The Reflectionary Constraint: Furthermore, because the room features floor-to-ceiling mirrors on all walls, we must also account for vertical symmetry. Two arrangements are considered identical if one is a reflection of the other. Answer the following two questions. (1) Assuming that A1, A2, and A3 are distinct sculptures, calculate the total number of ways that the 10 sculptures can be arranged on the pedestals while satisfying all three conditions. (20%)

相關申論題

相關試卷