課程名稱︰統計學上
課程性質︰森林系必修
課程教師︰關秉宗
開課學院：生農學院
開課系所︰神經認知學程 森林環境暨資源學系
考試日期（年月日）︰November 13, 2008
考試時限（分鐘）：三節課(234到12點)
是否需發放獎勵金：是的
老師考試自由，open book，完全沒人監考，要交卷就自己交到講桌，就可以離開了
試題 :
Please include the calculation details in your answers
1. A box contains 1000 light bulbs. The probability that there is at least 1
defective item in the box is 0.1, and the probability of having at least 2
defective bulbs is 0.05. Please find the probability for the following events.
A. The box has no defective light bulb. (5%)
B. The box has exactly 1 defective bulb. (5%)
C. The box has at most 1 defecctive light bulb. (5%)
2. Let X be a r.v. with pdf f(x)=(5-x^2)/15 , x=-2,-1,0,1,2; f(x)=0 elsewhere.
Please find
(a)P(X<=0) (b)P(X<0) (c)P(X<=1) (d)P(X<=1.5) (e)P(│X│<=1)
(f)P(│X│<1) (g)E(X) (h)VAR(X) (5% each)
3. Let X be a r.v. that represents the number of defects on a IC board with
pdf P(X=i)=c/(i+1), i=0,1,2,3,4 Please find
(a) The constant c such that f(x) will be a proper pdf (5%)
(b) The mean and variance of X (5%)
4. Let X be a r.v. with pdf f(x)=1/(b-a), a<=x<=b
(a) Please find the VAR of X (5%)
(b) Please find the c.d.f of X (5%)
5. Please find the mean and variance of the following pdf (5% each)
(a) f(x)=1/5, x=5,10,15,20,25 (b)f(x)=1, x=5
(c) f(x)= 3! 1 3
──── * (──)^x *(──)^3-x
x!(3-x)! 4 4 , x=0,1,2,3
6. Using binomial theorem, please verify that the pdf of a binomial
distrubution sums to unity. (10%)
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