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研究所、轉學考(插大)◆統計學
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95年 - 95 國立交通大學管碩士班考試入學試題_交通運輸研究所、運輸科技與管理學系：統計學#124791
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一、(10%) Consider the c.d.f. given by
Sketch f(x) and F(x).
其他申論題
(b) 請問如何交易此新選擇權 A, 可使原投資組合 Vega 中性與 Delta 中性 (Neutral)? (3 分)
#530835
(c) 如果尚有一可交易的選擇權 B, 每一單位 Delta= 0.1、Gamma=0.5 與 Vega=0.6, 請問如何交易此新二種選擇權, 可使原投資組合 Vega 中性、Gamma 中性與 Delta 中性 (Neutral)? (4 分)
#530836
(a) 某一年期固定對浮動利率交換 (Fixed-for-floating interest swap) 契約, 本金$1 million 且半年支付一次, 持有人收固定利率付浮動利率, 年固定利率 10%, 浮動利率參照 LIBOR, 當預期 LIBOR零息利率曲線為水平年利率 6%, 請問該利率交換契約價值多少? (可單利計算) (5 分)
#530837
(b) 美國 CBOT 交易所 August 1 時某債券投資組合價值$10 million, 該債券投資組合存續期間(Duration) 為 7.1 年, 若十二月公債期貨今天的報價為 91-12 (每單位價值$1,000), 而最便宜可交割債券 (Cheapest-to-deliver bond) 的存續期間為 8.8 年, 為期最小化債券投資組合價格對利率變化的影響, 擬執行存續期間基礎之避險策略 (Duration-based hedging strategies), 請問應買賣多少期貨契約? (5 分)
#530838
二、(10%) With X₁ denoting the amount of gasoline stocked in a bulk tank at the beginning of a week and X₂ the amount sold during the week, Y = X₁ - X₂ represents the amount left over at the end of the week. Find the mean and variance of Y if the joint function of (X₁, X₂) is given byf(x₁, x₂) = 3x₁ 0 ≤ x₂ ≤ x₁ ≤ 1 = 0 elsewhere
#530840
(1) the two components operate in series (5%)
#530841
(2) the two components operate in parallel (5%)
#530842
四、(10%) A taxi is traveling back and forth along a linear route of k miles for servicing customers who call for a ride. Customer calls may occur randomly at any location on the route. Suppose that the taxi will respond to and go picking the customer immediately when it receives his/her call. Find the average moving distance (in miles) of the taxi from where it answered a call to the customer?
#530843
(1) Find the probability that exactly two of the three plants process more than 4 tons on a given day? (5%)
#530844
(2) For a particular plant, how much raw sugar should be stocked for that plant each day so that the chance of running out of product is only 0.05? (5%)
#530845
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