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近期考題
4. (Total-18%) Consider a binary symmetric channel with input X, output Y, and
transition probability a. More specifically, as shown in the figure below, the input
and output of the channel may be "0" or "1", P(Y=0|X=0)=
P(Y = 1|X = 1) = 1 - a and P(Y = 1|X = 0) = P(Y=0|X=0) = a. The
prior probability is P(X = 0) = p.
【題組】
(d) (5%) Suppose the prior probability is not known in advance. We manage to
produce an estimated prior probability 
which may or may not
be equal to the true prior probability P(X = 0) = p. In this case, the cross-
entropy between the true and estimated prior distributions P and
is
defined by 
, which can be
considered as an approximated entropy of X. Please show that the cross-
entropy 
is always no less than the true entropy H(X) of X, i.e. 
(Hint: You may use the Jensen's inequality: plog2 a + (1 -p)log2≤ b ＜
log2(pa +(1 -p)b) for 0 ≤p ≤ 1, a ＞ 0, and b ＞0.)
(A)訓練前應根據業務員的特質進行分析， 以給予適切的訓練
(B)若通訊處訓練活動與公司活動、訓練衝突，應以通訊處為主
(C)向業 務員表達訓練的目的
(D)記錄業務員訓練後的成果表現，並定期追蹤
(A) For any orthogonal n x n matrix G, we have that Gs is orthogonal to u
(B) For any orthogonal n x n matrix G, we have that Gu is orthogonal to both s and t
(C)s is orthogonal to t
(D) s + t is orthogonal to u
(E) None of the preceding statements are true [cos(t)
明（97）年起，分配給員工之股票須按費用認列，不得再作為盈餘分配。經濟日報
記者於今（96）年 11 月 26 日以“企業留才 搶發認股權證＂一文宣稱新方式「衝
擊企業獲利」，並報導一家會計師事務所認為企業可採行之因應方式： 1.多發現金、少發股票。 2.發認股權憑證給員工，而不發股票給員工。 3.買回庫藏股，轉讓給員工。 4.由大股東將自己持有的公司股票交付信託，將孳息發給員工。5.以關係企業的股票發給員工，惟該等關係企業尚未上市上櫃。 試作：【題組】 ⑴請說明台積電 95 年度之盈餘如何分配？（5 分）
【題組】19. We create a binary search tree by considering the integers one by one, starting with the first one, 30. Which of the following are true?
(A) The node for 75 is a leaf node；
(B) The node for 42 is an internal node；
(C)The node for 99 has only one child；
(D) The height of the resulting tree is 5.
第四題：
某畜產試驗所想調查四種牧草是否影響乳牛產乳量，考量飼養牧場管理差異，選取八個
牧場為區集(block)，每個牧場隨機抽取四頭乳牛，並隨機分配餵以四種牧草，並記錄每周產
乳量（單位：公斤），根據所收集資料得到下列的變方分析表(ANOVA)：（假設每周產乳量為
常態分布）；註：F 分布第 95 個百分位（即 Fα=0.05）：F(2,30)=3.32, F(3,30)=2.92,
F(2,20)=3.49, F(3,20)=3.10, F(3,21)=3.07, F(3,31)=2.91, F(8,24)=2.36, F(7,30)=2.33,
F(7,31)=2.32, F(7,20)=2.51, F(7,21)=2.49, F(8,21)=2.42，請回答下列問題：
【題組】⑶牧草是否有顯著差異？（顯著水準 α=0.05）【5 分】
be 3x4 matrix. (20 points)