课程名称︰统计学上 课程性质︰森林系必修 课程教师︰关秉宗 开课学院：生农学院 开课系所︰神经认知学程 森林环境暨资源学系 考试日期（年月日）︰November 13, 2008 考试时限（分钟）：三节课(234到12点) 是否需发放奖励金：是的 老师考试自由，open book，完全没人监考，要交卷就自己交到讲桌，就可以离开了 试题 : 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%) -- 离开情感， 音乐只是空气的振动，图画只是着色的纸张 文学只是串联的文字，性爱只是活塞运动。 --

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