电大工程数学试卷及答案小抄参考

1、专业好文档一、单项选择题（每小题3分，共15分）在每小题列出的四个选项中只有一个是符合题目要求的，请将其代码填在题后的括号内。错选或未选均无分。得分评卷人1某人打靶3发，事件ai 表示“击中i发”，i=0,1,2,3. 那么事件a=a1a2a3表示()。 a. 全部击中. b. 至少有一发击中. c. 必然击中 d. 击中3发2对于任意两个随机变量x和y，若e(xy)=e(x)e(y)，则有()。a. x和y独立。 b. x和y不独立。c. d(x+y)=d(x)+d(y) d. d(xy)=d(x)d(y)3下列各函数中可以作为某个随机变量的概率密度函数的是（ ）。a 。 b. c. d.

2、，4设随机变量x, y, , 则有（ ）a. 对于任意的, p1=p2 b. 对于任意的, p1 p25设x为随机变量，其方差存在，c为任意非零常数，则下列等式中正确的是（） ad(x+c)=d(x). b. d(x+c)=d(x)+c. c. d(x-c)=d(x)-c d. d(cx)=cd(x)得分二、填空题（每空3分，共15分）评卷人6 设3阶矩阵a的特征值为-1，1，2，它的伴随矩阵记为a*， 则|a*+3a2e|= 。7设a= ，则= 。8设有3个元件并联，已知每个元件正常工作的概率为p，则该系统正常工作的概率为 。9设随机变量的概率密度函数为，则概率 。10设二维连续型随机变量的

3、联合概率密度函数为，则系数 。得分三、计算题（每小题10分，共50分）评卷人11求函数的傅氏变换 (这里)，并由此证明：12发报台分别以概率0.6和0.4发出信号“1”和“0”。由于通讯系统受到干扰，当发出信号“1”时，收报台未必收到信号“1”，而是分别以概率0.8和0.2收到信号“1”和“0”；同时，当发出信号“0”时，收报台分别以概率0.9和0.1收到信号“0”和“1”。求（1）收报台收到信号“1”的概率；（2）当收报台收到信号“1”时，发报台确是发出信号“1”的概率。13设二维随机变量的联合概率函数是求：（1）常数c；（2）概率p(xy )；（3）x与y相互独立吗？请说出理由。14将n个

4、球随机的放入n个盒子中去，设每个球放入各个盒子是等可能的，求有球盒子数x的数学期望。15设一口袋中依此标有1，2，2，2，3，3数字的六个球。从中任取一球，记随机变量x为取得的球上标有的数字，求(1)x的概率分布律和分布函数。(2)ex得分四、证明题（共10分）评卷人16.设a=(a1,a2,an)t，a10,其长度为a，又a=aat,(1) 证明a2=a2a；(2) 证明a是a的一个特征向量，而0是a的n-1重特征值；(3) a能相似于对角阵吗？若能,写出对角阵.得分五、应用题（共10分）评卷人17.设在国际市场上每年对我国某种出口商品的需求量x是随机变量,它在2000,4000( 单位：吨

5、 )上服从均匀分布，又设每售出这种商品一吨，可为国家挣得外汇3万元，但假如销售不出而囤积在仓库，则每吨需保养费1万元。问需要组织多少货源，才能使国家收益最大。参考答案及评分标准一、 选择题（每小题3分，共15分）1b2c3d4a5a 二、 填空题（每小题3分，共15分）6. 9 7. 1 8. 1(1p)3 9. 3/4 10. 12三、计算题（每题10分，共50分）11.解答：函数f(t)的付氏变换为：f(w)= （3分） = (2分)由付氏积分公式有f(t)=f(w)= (2分) = = （2分）所以 （1分）12.解答: 设 a1=“发出信号1”，a0=“发出信号0”，a=“收到信号1”

6、 （2分）(1)由全概率公式 （1分）有 p(a)=p(a|a1)p(a1)+p(a|a0)p(a0) （2分） =0.8x0.6+0.1 x0.4=0.52 （1分）(2)由贝叶斯公式 （1分）有 p(a1|a)=p(a|a1)p(a1)/ p(a) （2分） =0.8x0.6/0.52=12/13 （1分）13.解答:(1) 由联合概率密度的性质有即 （2分）从而 c=8 （2分）(2) （2分）(3) 当x0时， （2分）当x=0时, 同理有 （1分）因 故x与y相互独立 （1分）14.解答：设 i =1,2,n (2分)则 (1分)因 (2分) (2分)因而 (2分)所以 (2分)15

7、.解答：（1）随机变量的取值为1，2，3。 （1分）依题意有： （3分）的分布函数 （1分）由条件知：当时， （1分） 当时， （1分）当时， （1分）当时， （1分）（2）ex=1 x 1/6+2 x 3/6+3 x 2/6= 13/6 （1分）四、证明题（共10分）(1) a2=aataat=ata aat =a2a （2分）(2)因 aa= aat a=ataa= a2a （2分）故a是a的一个特征向量。又a对称，故a必相似于对角阵 （1分）设a diag(1,2,n)=b, 其中1,2,n是a的特征值 (1分)因rank(a)=1, 所以 rank(b)=1 (1分)从而1,2,n中必

8、有n-1个为0, 即0是a的n-1重特征值 （1分）(3) a对称，故a必相似于对角阵，=diag(a2, 0,0) (2分)五、应用题（共10分）解答:设y为预备出口的该商品的数量，这个数量可只介于2000与4000之间，用z表示国家的收益（万元）, （1分）则有 （4分）因 x服从r(2000,4000), 故有 (1分)所以 =( y2 7000y + 4106 ) /1000 (3分)求极值得 y=3500 (吨) (1分)if we dont do that it will go on and go on. we have to stop it; we need the courag

9、e to do it.his comments came hours after fifa vice-president jeffrey webb - also in london for the fas celebrations - said he wanted to meet ivory coast international toure to discuss his complaint.cska general director roman babaev says the matter has been exaggerated by the ivorian and the british

10、 media.blatter, 77, said: it has been decided by the fifa congress that it is a nonsense for racism to be dealt with with fines. you can always find money from somebody to pay them.it is a nonsense to have matches played without spectators because it is against the spirit of football and against the

11、 visiting team. it is all nonsense.we can do something better to fight racism and discrimination.this is one of the villains we have today in our game. but it is only with harsh sanctions that racism and discrimination can be washed out of football.the (lack of) air up there watch mcayman islands-ba

12、sed webb, the head of fifas anti-racism taskforce, is in london for the football associations 150th anniversary celebrations and will attend citys premier league match at chelsea on sunday.i am going to be at the match tomorrow and i have asked to meet yaya toure, he told bbc sport.for me its about

13、how he felt and i would like to speak to him first to find out what his experience was.uefa hasopened disciplinary proceedings against cskafor the racist behaviour of their fans duringcitys 2-1 win.michel platini, president of european footballs governing body, has also ordered an immediate investig

14、ation into the referees actions.cska said they were surprised and disappointed by toures complaint. in a statement the russian side added: we found no racist insults from fans of cska.baumgartner the disappointing news: mission aborted.the supersonic descent could happen as early as sunda.the weathe

15、r plays an important role in this mission. starting at the ground, conditions have to be very calm - winds less than 2 mph, with no precipitation or humidity and limited cloud cover. the balloon, with capsule attached, will move through the lower level of the atmosphere (the troposphere) where our d

16、ay-to-day weather lives. it will climb higher than the tip of mount everest (5.5 miles/8.85 kilometers), drifting even higher than the cruising altitude of commercial airliners (5.6 miles/9.17 kilometers) and into the stratosphere. as he crosses the boundary layer (called the tropopause),e can expec

17、t a lot of turbulence.the balloon will slowly drift to the edge of space at 120,000 feet ( then, i would assume, he will slowly step out onto something resembling an olympic diving platform.below, the earth becomes the concrete bottom of a swimming pool that he wants to land on, but not too hard. st

18、ill, hell be traveling fast, so despite the distance, it will not be like diving into the deep end of a pool. it will be like he is diving into the shallow end.skydiver preps for the big jumpwhen he jumps, he is expected to reach the speed of sound - 690 mph (1,110 kph) - in less than 40 seconds. like hitting the top of the water, he will begin to slow as he approaches the more dense air closer to earth. but this will not be enough to stop him completely.if he goes too fast or spins out of control, he has a stabilization parachute