问题 解答题

现有4个人去参加娱乐活动,该活动有甲、乙两个游戏可供参加者选择,为增加趣味性,约定:每个人通过掷一枚质地均匀的骰子决定自己去参加哪个游戏,掷出点数为1或2的人去参加甲游戏,掷出点数大于2的人去参加乙游戏。

(1)求这4个人中恰有2人去参加甲游戏的概率;

(2)求这4个人中去参加甲游戏的人数大于去参加乙游戏的人数的概率;

(3)用X,Y分别表示这4个人中去参加甲、乙游戏的人数,记ξ=|X-Y|,求随机变量ξ的分布列与数学期望Eξ。

答案

解:依题意,这4个人中,每个人去参加甲游戏的概率为,去参加乙游戏的人数的概率为

设“这4个人中恰有2人去参加甲游戏”为事件Ai(i=0,1,2,3,4),

∴P(Ai)=

(1)这4个人中恰有2人去参加甲游戏的概率为P(A2)=

(2)设“这4个人中去参加甲游戏的人数大于去参加乙游戏”为事件B,则B=A3∪A4

∴P(B)=P(A3)+P(A4)=

(3)ξ的所有可能取值为0,2,4,

由于A1与A3互斥,A0与A4互斥,

故P(ξ=0)=P(A2)=

P(ξ=2)=P(A1)+P(A3)=

P(ξ=4)=P(A0)+P(A4)=

∴ξ的分布列是

Eξ=0×+2×+4×=

填空题

Third-generation mobile phones, known as 3G, are the next big step for the telecom industry. Data speed in 3G networks is much quicker than that in present technology. This means users can have high-speed Internet access and enjoy video and CD-quality music on their phones.

"Mobile data is not a dream; it’s not an option but a requirement," said Len Lauer, head of a US communications company, Sprint PCS, at a 3G conference in Bangkok earlier this month.

With 3G, you can forget about text messages telling you yesterday’s news; a 3G phone can receive video news programs, updated four times a day. Internet access will also be much quicker, making it easier to surf the Web on your phone than on your computer at home.

Don’t worry about getting lost. 3G phones offer map services so you can find a new restaurant just by pressing a few keys on your handset.

However, the most impressive part of 3G technology is video calling. With live two-way video communication, you can have face-to-face talks with friends and family on your mobile phone.

Many European countries have already launched the service. In May 2000 the US Government issued five license to run 3G wireless services, while the first 3G phones arrived in Italy in March this year.

International telecom companies can’t wait to sell 3G in China, the world’s largest mobile telecommunications market. But they will have to be patient. At the moment, China is busy testing its 3G-based technologies, networks and services. This will be followed by a trial period before the phones can finally hit the shops.

"We need to create a pool of 3G customers before the large-scale commercial launch of the service," said Fan Yunjun, marketing manager for Beijing Mobile. "We expect that the 3G licenses will be issued late next year.

Third-generation mobile phones (3G mobile phones)
(1)
  • a. Data speed: (2) than present technology
  • b. Video and (3) music
  • c. Video news programs: (4) four times a day
  • d. Internet access: quicker and (5)
Impressive

functions

a. Offer (6) services, helping you find your wayb. Provide two-way video (7)
3G phones in Chinaa. China is busy (8) its 3G-based technologies, networks and services.b. 3G phones should go through a (9) period before being put into market.c. 3G phones are expected to be seen (10) next year.

第(10)空应填()

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