8. Given the following linear regression model:
Υ₁ = β₁Χ₁+ εᵢ where i = 1, 2, 3, ...., n
(2) Show that the maximum likelihood estimator of β₁ is unbiased. (5%)
(1) Assume that the error terms εᵢ are independent N(0, σ²) and that σ² is known. State the likelihood function for the n sample observations on Y and obtain the maximum likelihood estimator of β₁. Is it the same as the least squares estimator of β₁? (10%)
7. An equipment manufacturer has developed a new electrical product. He
claims that the product has a mean life length of 10,000 hours, with a standard
deviation of 150 hours. A consumer tested 16 random samples of the product
and obtained a mean life length of 9,775 hours. Evaluate at the 0.05 level of
significance whether the life length announcement for the new product is
reliable ? (12%)
100. 請問這是引擎中的哪一個零件?(A)飛輪 (B)曲軸 (C)連桿 (D)活塞。
99. 將汽缸的面積乘以衝程,即可得到汽缸的(A)排氣量(B)壓縮比 (C)爆發壓力(D)轉速。
98. 當今大型船舶所用的主機,絕大多數皆為以下何者?(A)汽油機 (B)燃氣渦輪機(C)柴油機(D)蒸汽渦輪機。
This is a large modal.