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1、专业好文档一、 填空题（每题2分，共20分）1、记三事件为A，B，C. 则用A，B，C及其运算关系可将事件，“A，B，C中只有一个发生”表示为 .2、匣中有2个白球，3个红球。 现一个接一个地从中随机地取出所有的球。那么，白球比红球早出现的概率是 2/5 。3、已知P(A)=0.3，P（B）0.5，当A，B相互独立时，。4、一袋中有9个红球1个白球，现有10名同学依次从袋中摸出一球（不放回），则第6位同学摸出白球的概率为 1/10 。5、若随机变量在区间 上服从均匀分布，则对以及任意的正数，必有概率 6、设服从正态分布，则 N ( 3-2 , 42 ) .7、设8、袋中装有5只球，编号为1，2
2、，3，4，5，在袋中同时取出3只，以表示取出3只球中的最大号码。则的数学期望 4.5 。9、设随机变量的分布律为XY12310.120.100.2820.1800.12300.150.05则条件概率 2/5 .10、设来自正态总体, ,当常数= 1/4 时，服从分布。二、计算题（每小题10分，共70分）1、三台机器因故障要人看管的概率分别为0.1，0.2，0.15，求：（1）没有一台机器要看管的概率（2）至少有一台机器不要看管的概率（3）至多一台机器要看管的概率解：以Aj表示“第j台机器需要人看管”，j=1，2，3，则:P( A1 ) = 0.1 , P( A2 ) = 0.2 , P( A3
3、 ) = 0.15 ,由各台机器间的相互独立性可得2、甲袋中有n只白球、m只红球；乙袋中有N只白球、M只红球。今从甲袋任取一球放入乙袋后，再从乙袋任取一球。问此球为白球的概率是多少？解：以W甲表示“第一次从甲袋取出的为白球”，R甲表示“第一次从甲袋取出的为红球”， W乙表示“第二次从乙袋取出的为白球”，则所求概率为 3、设随机变量X的概率密度为, 试求（1）常数A;(2) 分布函数; (3) 概率。解：（1） 由归一性可得：，从而 4、（1）已知X的分布律为-1 0 1 2 3 计算。（5分）解：（2）、设，求的概率密度.（5分） 解：Y的密度函数为：5、设的概率密度为. (1) 试求分布函数
4、； (2) 求概率其中区域由轴, 轴以及直线所围成.解: 6、设二维随机变量的概率密度为,求常数及边缘概率密度.并讨论随机变量的相互独立性。解：由归一性知：显然 ，故X与Y不相互独立。7、设总体的概率密度为, 其中为未知参数. 若是来自母体的简单子样，试求的矩估计与极大似然估计.解：（1） 令 解得的矩估计为 （2）似然函数 对数似然函数 令 解得的极大似然估计为 三、证明题（每题5分，共10分） 1、为来自总体X的样本，证明当时，为总体均值的无偏估计。证明：设总体均值= ，由于为来自总体X的样本，因此 而 为总体均值的无偏估计，故应该有 从而 2、设是相互独立的随机变量，它们分别服从参数为的
5、泊松分布，证明服从参数为的泊松分布。证明：由题知 ，即 令，且由的相互独立性可得： 即 服从参数为的泊松分布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 p
17、reparation 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.The Kiwis are a lot less experienced but winning a dramatic match like their semi-final against England will do wonders for their confidence.They defeated Australia in the Four Nations final in 2010 and the last World Cup, and know they can rise to the big occasion.
