[試題] 97下 康明昌 微積分乙 期末考

[saiga12416 (碎牙)]

課程名稱︰微積分乙
課程性質︰系定必修
課程教師︰康明昌
開課學院：醫學院
開課系所︰醫學系
考試日期（年月日）︰98/6/16
考試時限（分鐘）：110分鐘
是否需發放獎勵金：是
（如未明確表示，則不予發放）

試題 :
(1) 5 fair coins are flipped. If the outcome are assumed independent. Find
    the cumulative distributions of the number ofheads obtained.(15%)

(2) Suppose that you toss a perfect coin repeatedly until a head turns up.
    What is the average number of tosses to finish this game? (Hint: What may
    be the "good" random variable X? What should you find E(X) or Var(X)? )
    (15%)

(3) (Approving a new drug) It is known that a chance of 90% that the goverment
    will approve a new drug if the results of testing show no side effect of
    the drug. On the other hand, only a chance of 40% remains for the approval
    if the tests show some side effect. Physician of the drug company believe
    that there is only a 0.1 probability that the tests will show side effects
    of the drug. What is the probability that the drug will be approves? (15%)

(4) Let the joint density function of two random variables X and Y be
    f(x,y)={ (12/5)xy(1+y) ,if 0<=x<=1, 0<=y<=1
           { 0 , otherwise
    Find E(X), E(Y) and Cov(X,Y)  (15%)

(5) Let X1,X2,X3.....,X625 be a sequence of i.i.d. random variables. Let the
    probability density function of X1 is
    f(x)={ 3(1-x)^2 , if 0<=x<+1
         { 0        , otherwise
    1. Find E(X1) and Var(X1)               (10%)
    2. Use the Central Limit Theorem and the table of Φ(x) to approximate the
       value of P(X1+X2+.....+X625<=170).   (15%)

(6) A multiple-passenger taxi policy is enforced at some city. Every taxi
    should wait until 4 passengers are aquired or a period of 10 minutes has
    passed since the first passenger stepped into the car. Passengers arrive
    according to a Poisson process with an average of 1 passenger every 3
    minutes.
    1. If you are the first passenger to  get in to a car, what is the
       probability that you will have to wait 10minutes before the taxi gets
       underway?    (10%)
    2. If you are the first passenger of a taxi and you have been waiting
       there for 5 minutes. During this period 2 other passengers entered
       the taxi. What is the probability that you will wait another 5 minutes
       before the car gets underway?   (15%)
       (Hint: You can provide your answer in terms of e^3, e^10, e^5,e^(10/3).
       ....., without replacing them into decimals.)

--
※ 發信站: 批踢踢實業坊(ptt.cc)
◆ From: 140.112.242.161
※ 編輯: saiga12416      來自: 140.112.242.161      (06/16 15:22)
→ aa124816    :阿...晚一步
→ saiga12416  :來不及了~
推 dhcs        :兩位都缺P幣缺很大嗎 XDD
→ aa124816    :你要附註一下有給表
推 ALegmontnick:done