電大概率統(tǒng)計(jì)試題及答案(本科完整版)小抄參考

1、專業(yè)好文檔一、 填空題（每題2分，共20分）1、記三事件為a，b，c. 則用a，b，c及其運(yùn)算關(guān)系可將事件，“a，b，c中只有一個(gè)發(fā)生”表示為 .2、匣中有2個(gè)白球，3個(gè)紅球。 現(xiàn)一個(gè)接一個(gè)地從中隨機(jī)地取出所有的球。那么，白球比紅球早出現(xiàn)的概率是 2/5 。3、已知p(a)=0.3，p（b）0.5，當(dāng)a，b相互獨(dú)立時(shí)，。4、一袋中有9個(gè)紅球1個(gè)白球，現(xiàn)有10名同學(xué)依次從袋中摸出一球（不放回），則第6位同學(xué)摸出白球的概率為 1/10 。5、若隨機(jī)變量在區(qū)間 上服從均勻分布，則對以及任意的正數(shù)，必有概率 6、設(shè)服從正態(tài)分布，則 n ( 3-2 , 42 ) .7、設(shè)8、袋中裝有5只球，編號為1，2

2、，3，4，5，在袋中同時(shí)取出3只，以表示取出3只球中的最大號碼。則的數(shù)學(xué)期望 4.5 。9、設(shè)隨機(jī)變量的分布律為xy123820.1800.12300.150.05則條件概率 2/5 .10、設(shè)來自正態(tài)總體, ,當(dāng)常數(shù)= 1/4 時(shí)，服從分布。二、計(jì)算題（每小題10分，共70分）1、三臺機(jī)器因故障要人看管的概率分別為0.1，0.2，0.15，求：（1）沒有一臺機(jī)器要看管的概率（2）至少有一臺機(jī)器不要看管的概率（3）至多一臺機(jī)器要看管的概率解：以aj表示“第j臺機(jī)器需要人看管”，j=1，2，3，則:p( a1 ) = 0.1 , p( a2 ) = 0.2 , p( a3

3、 ) = 0.15 ,由各臺機(jī)器間的相互獨(dú)立性可得2、甲袋中有n只白球、m只紅球；乙袋中有n只白球、m只紅球。今從甲袋任取一球放入乙袋后，再從乙袋任取一球。問此球?yàn)榘浊虻母怕适嵌嗌?？解：以w甲表示“第一次從甲袋取出的為白球”，r甲表示“第一次從甲袋取出的為紅球”， w乙表示“第二次從乙袋取出的為白球”，則所求概率為 3、設(shè)隨機(jī)變量x的概率密度為, 試求（1）常數(shù)a;(2) 分布函數(shù); (3) 概率。解：（1） 由歸一性可得：，從而 4、（1）已知x的分布律為-1 0 1 2 3 計(jì)算。（5分）解：（2）、設(shè)，求的概率密度.（5分） 解：y的密度函數(shù)為：5、設(shè)的概率密度為. (1) 試求分布函數(shù)

4、； (2) 求概率其中區(qū)域由軸, 軸以及直線所圍成.解: 6、設(shè)二維隨機(jī)變量的概率密度為,求常數(shù)及邊緣概率密度.并討論隨機(jī)變量的相互獨(dú)立性。解：由歸一性知：顯然 ，故x與y不相互獨(dú)立。7、設(shè)總體的概率密度為, 其中為未知參數(shù). 若是來自母體的簡單子樣，試求的矩估計(jì)與極大似然估計(jì).解：（1） 令 解得的矩估計(jì)為 （2）似然函數(shù) 對數(shù)似然函數(shù) 令 解得的極大似然估計(jì)為 三、證明題（每題5分，共10分） 1、為來自總體x的樣本，證明當(dāng)時(shí)，為總體均值的無偏估計(jì)。證明：設(shè)總體均值= ，由于為來自總體x的樣本，因此 而 為總體均值的無偏估計(jì)，故應(yīng)該有 從而 2、設(shè)是相互獨(dú)立的隨機(jī)變量，它們分別服從參數(shù)為的

5、泊松分布，證明服從參數(shù)為的泊松分布。證明：由題知 ，即 令，且由的相互獨(dú)立性可得： 即 服從參數(shù)為的泊松分布winger tuivasa-sheck, who scored two tries in the kiwis 20-18 semi-final win over england, has been passed fit after a lower-leg injury, while slater has been named at full-back but is still recovering from a knee injury aggravated against usa.bo

6、th sides boast 100% records heading into the encounter but australia have not conceded a try since josh charnleys effort in their first pool match against england on the opening day.aussie winger jarryd hayne is the competitions top try scorer with nine, closely followed by tuivasa-sheck with eight.

7、but it is recently named rugby league international federation player of the year sonny bill williams who has attracted the most interest in the tournament so far.the kiwi - with a tournament high 17 offloads - has the chance of becoming the first player to win the world cup in both rugby league and

8、 rugby union after triumphing with the all blacks in 2011.id give every award back in a heartbeat just to get across the line this weekend, said williams.the (lack of) air up there watch mcayman islands-based webb, the head of fifas anti-racism taskforce, is in london for the football associations 1

9、50th 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 how he felt and i would like to speak to him first to find out what his experience was.uefa has

10、opened 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 investigation into the referees actions.cska said they were surprised and disappointed by toures compla

11、int. 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 weather plays an important role in this mission. starting at the ground, conditions have to be very

12、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 day-to-day weather lives. it will climb higher than the tip of mount everest (5.5 miles/8.85 ki

13、lometers), 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 expect a lot of turbulence.the balloon will slowly drift to the edge of space at 120,000 feet ( the

14、n, i would assume, he will slowly step out onto something resembling an olympic diving platform.they blew it in 2008 when they got caught cold in the final and they will not make the same mistake against the kiwis in manchester.five years ago they cruised through to the final and so far history has

15、repeated itself here - the last try they conceded was scored by englands josh charnley in the opening game of the tournament.that could be classed as a weakness, a team under-cooked - but i have been impressed by the kangaroos focus in their games since then.they have been concentrating on the sort

16、of stuff that wins you tough, even contests - strong defence, especially on their own goal-line, completing sets and a good kick-chase. theyve been great at all the unglamorous stuff that often goes unnoticed in the stands but not by your team-mates.it is as though their entire tournament has been preparation for the final.in johnathan thurston, cooper cronk, cameron smith and either billy slater or greg inglis at full-back they have a spine that is unmatched in rugby league. they have played in so many high-pressure games - a priceless asset going into saturday.