应得客最新考试题

两台同样自动记录仪,每台无故障工作的时间服从参数为 5 的指数分布；首先开动其中一台,当其发生故障时停用而另一台自行开动.试求两台记录仪无故障工作的总时间T 的概率密度 f (t ) 、数学期望和方差.

已知连续型随机变量 X 的概率密度为

已知随机变量 X 服从参数为 2 的泊松分布，且随机变量Z=3X-2,则 EZ =________ .

设随机变量 X 服从参数为 1 的指数分布，则

设 X 表示 10 次独立重复射击命中目标的次数,每次射中目标的概率为 0.4,则

甲乙两人独立地各进行两次射击，假设甲的命中率为 0.2，乙的为 0.5，以 X 和Y 分别表示甲和乙的命中次数，试求 X 和Y 的联合概率分布

设 X 是一个随机变量，其概率密度为

一电子仪器由两个部件构成，以 X 和 Y分别表示；两个部件的寿命（单位：千小时），已知 X 和Y 的联合分布函数为

已知随机变量 X 服从二项分布，且 EX =2.4 ，DX =1.44, 则二项分布的参数 n， p的值为

设二维随机变量(,) X Y 的概率密度为

已知随机变量 X 和Y 的联合概率密度为

设两个相互独立的随机变量 X 和Y 的方差分别为 4 和 2,则随机变量3X -2Y 的方差是（）

设随机变量 X ,Y 相互独立，其概率密度函数分别为

设二位随机变量(X， Y) 的概率密度为

设相互独立的两个随机变量 X 、Y 具有同一分布律,且 X的分布律为

设 X 和Y 为两个随机变量,且

设随机变量 X Y 和相互独立，其概率分布为

设两个随机变量 X 与 Y 相互独立且同分布

在区间（0,1）中随机地取两个数，则事件“两数之和小于6/5 ”的概率为______ .

从 0,1,2，9 等十个数字中任意选出三个不同的数字，试求下列事件的概率： A1  三个数字中不含0和5 ； A2  三个数字中不含0或5；A3  三个数字中含0但不含5

点落在半圆内任何区域的概率与该区域的面积成正比，则原点与该点连线与 x 轴的夹角小于 /4 的概率为 ________

将C，C，E，E，I， N，S等七个字母随机地排成一行,那么,恰好排成 SCIENCE 的概率为__________

考虑一元二次方程 x 2Bx  C  0 ,其中 B、C 分别是将一枚色子(骰子)接连掷两次先后出现的点数。求该方程有实根的概率 p 和有重根的概率q。

三个箱子，第一个箱子中有 4 个黑球 1 个白球，第二个箱子中有 3 个黑球 3 个白球，第三个箱子中有 3 个黑球 5 个白球.现随机地取一个箱子，再从这个箱子中取出 1 个球，这个球为白球的概率等于________ .已知取出的球是白球，此球属于第二个箱子的概率为________ .

假设有两箱同种零件：第一箱内装 50 件，其中 10 件一等品；第二箱内装 30 件，其中 18 件一等品，现从两箱中随意挑出一箱，然后从该箱中先后随机取两个零件（取出的零件均不放回）.试求：（1）先取出的零件是一等品的概率 p ；（2）在先取出的零件是一等品的条件下，第二次取出的零件仍然是一等品的条件概率 q

已知随机变量 X 的概率分布为

玻璃杯成箱出售，每箱 20 只，假设各箱含 0,1,2 只残次品的概率相应为 0.8,0.1 和 0.1 一顾客欲购一箱玻璃杯，在购买时，售货员随意取一箱，而顾客随机地察看 4 只：若无残次品，则购买下该箱玻璃杯，否则退回.试求：（1）顾客买下该箱的概率 ；（2）在顾客买下的一箱中，确认没有残次品的概率  ；

设随机变量 X 的分布函数为

在电源电压不超过 200 伏，200～240 伏和超过 240 伏三种情

一汽车沿一街道行驶,需要通过三个均设有红绿信号灯的路口,每个信号灯为红或绿与其他信号灯为红或绿相互独立,且红绿两种信号显示的时间相等,以X 表示该汽车首次遇到红灯前已通过的路口的个数.求 X 的概率分布

已知随机事件 A 的概率 P ( A) 0.5 ，随机事件 B 的概率

假设随机变量 X 的绝对值不大于 1；

设随机变量 X 在[2,5]上服从均匀分布，现在对 X 进行三次独立观测，试求至少有两次观测值大于 3 的概率

甲、乙两人独立地对同一目标射击一次，其命中率分别为0.6 和 0.5，现已知目标被命中，则它是甲射中的概率为 ______________

某仪器装有三只独立工作的同型号电子元件，某寿命（单位：小时）都服从同一指数分布，概率密度为

设随机事件 A B, 及其和事件 A∪B 的概率分别是 0.4，

某地抽样调查结果表明，考生的外语成绩（百分制）近似服从正态分布，平均成绩为 72 分，96 分以上的占考生总数的2.3%，试求考生的外语成绩在 60 分至 84 分之间的概率.

一批产品有 10 个正品和 2 个次品，任意抽取两次，每次抽一个，抽出后不再放回，则第二次抽出的是次品的概率为 ________

假设一大型设备在任何长为t 的时间内发生故障的次数 N（t）服从参数为λt 的泊松分布. (1) 求相继两次故障之间时间间隔T 的概率分布； (2) 求在设备已无故障工作 8 小时的情形下,再无故障运行 8 小时的概率Q.

设 10 件产品有 4 件不合格品，从中任取两件，已知所取两件产品中有一件是不合格品，则另一件也是不合格品的概率为________

假设随机变量 X 的概率密度为

则P(B)=_______

假设一厂家生产的每台仪器,以概率 0.70 可以直接出厂；以概率 0.30 需进一步调试, 经调试后以概率 0.80 可以出厂；以概率 0.20 定为不合格品不能出厂.现该厂新生产了 n (n 2) 台仪器(假设各台仪器的生产过程相互独立).求： (1) 全部能出厂的概率 ； (2) 其中恰好有两台不能出厂的概率  ； (3) 其中至少有两台不能出厂的概率。

假设一批产品中一、二、三等品各占 60%，30%，10%，从中任意取出一件，结果不是三等品，则取到的是一等品的概率为_______

设随机变量 X 的概率密度函数为

设工厂 A 和工厂 B 的产品的次品率分别为 1%和 2%,现从由A 和 B 的产品分别占 60%和 40%的一批产品中随机抽取一件,发现是次品,则该次品属 A 生产的概率是_______

假设随机变量 X 在区间（1,2）上

一实习生用同一台机器连接独立地制造 3 个同种零件,第i 个

在区间（0,1）上服从均匀分布

袋中有 50 个乒乓球,其中 20 个是黄球,30 个是白球,今有两人依次随机地从袋中各取一球,取后不放回,则第二个人取得黄球的概率是________

假设一电路装有三个同种电器元件，其工作状态相互独立，且无故障工作时间都服从参数为λ＞0 的指数分布，当三个元件都无故障时，电路正常工作，否则整个电路不能正常工作.试求电路正常工作的时间T 的概率分布

设在一次试验中 A 发生的概率为 p ，现进行n次独立试验，则 A 至少发生一次的概率为________ ；而事件 A 至多发生一次的概率为________ .

已知随机变量 X 的概率密度函数

设三次独立试验中，事件 A 出现的概率相等.若已知 A 至少

设随机变量 X 服从均值为 10，均方差为 0.02 的正态分布.已知

一射手对同一目标独立地进行 4 次射击，若至少命中一次的

连续型随机变量取任何给定实数值的概率等于 0.( )

若两事件 A 和B 同时出现的概率 P AB   0，则________

设随机变量 X Y 与均服从正态分布，

对于任意两个事件 A 和B ，有 PA  B ________

以 A 表示事件“甲种产品畅

设 A 和 B 是任意两个概率不为零的互不相容事件，则下列结论中肯定正确的是（）

设当事件 A 与 B 同时发生时,事件C 必发生,则________

则下列选项成立的是（）

必然成立的是（）

Suppose Professor Smith asked you to plan a debate on the theme of city traffic. Write him an email to him.1) suggest a specific topic with your reasons, and2) tell him about your arrangements.You should write about 100 words on the ANSWER SHEET.Do not use your own name. Use “Zhang Wei” instead.Do not write your address. (10 points)

Suppose your cousin Li Ming has just been admitted to a university. Write him/her a letter to1) congratulate him/her, and2) give him/her suggestions on how to get prepared for university life You should write about 100 words on ANSWER SHEET 2.Do not sign your own name at the end of the letter. Use "Zhang Wei"instead.Do not write the address. (10 points)

Write an essay based on the following chart. In your writing, you should 1) interpret the chart and2) give your comment You should write at least 150 words Write your essay on ANSWER SHEET 2.(15points)

Suppose you are invited by Professor Williams to give a presentation about Chinese culture to a group of international students. Write a reply to1) accept the invitation, and2) introduce the key points of your presentation.You should write about 100 words on the ANSWER SHEET.Do not use your own name. Use “Li Ming” instead.Do not write your address. (10 points)

Suppose you have found something wrong with the electronic dictionary that you bought from an online store the other day, Write an email to the customer service center to1) Make a complaint and2) Demand a prompt solutionYou should write about 100words on ANSERE SHEET 2Do not sign your own name at the end of the letter, Use "Zhang Wei "instead.

Write an essay based on the following table. In your writing, you should1) describe the table, and2) give your commentsYou should write at least 150 words.Write your essay on the ANSWER SHEET. (15points)

Suppose you are planning a tour of historical site for a group of international students1) tell them about the site, and2) give them some tips for the tour.You should write about 100 words on the ANSWER SHEET.Do not use your own name. Use “Li Ming” instead. (10 points)

Suppose your class is to hold a charity sale for kids in need of help. Write your classmates anemail to1) inform them about the details, and2) encourage them to participate.You should write about 100 words on the ANSWER SHEET.You should write about 100 words on the ANSWER SHEET.Do not use your own name. Use “Li Ming” instead.Do not write your address. (10 points)

Suppose you won a translation contest and your friend, Jack, wrote an email to congratulate you and ask for advice on translation. Write him a reply to1) thank him, and2) give your advice.You should write about 100 words on the ANWSER SHEET.Do not use you own name. Use “Li Ming” instead.Do not write your address. (10 point)

Suppose you are going to study abroad and share an apartment with John, a local student. Write him an email to (1) tell him about your living habits, and (2) ask for advice about living there. You should write about 100 words on the ANSWER SHEET. Do not use your own name. Use “Li Ming” instead. Do not write your address. (10 points)

Write an essay based on the following chart. In your writing, you should (1) interpret the chart, and (2) give your comments. You should write about 150 words on the ANSWER SHEET. (15 points)

Suppose you have to cancel your travel plan and will not be able to visit Professor Smith. Write him an email to1) apologize and explain the situation, and2) suggest a future meeting.You should write about 100 words on the ANSWER SHEET.Do not use your own name. Use “Li Ming” instead.Do not write your address. (10 points)

It has been documented that during World War II, America’s armed forces once triedformation flight to save fuel.

Write an essay based on the chart below. In your writing, you should1)interpret the chart, and2)give your comments.You should write about 150 words on the ANSWER SHEET. (15 points)

Findings of the Stanford University researchers will promote the sales of new Boeing and Airbus aircraft.

Suppose your university is going to host a summer camp for high school students. Write a notice to(1) briefly introduce the camp activities, and(2) call for volunteers. You should write about 100 words on the ANSWER SHEET.Do not use your own name or the name of your university.Do not write your address. (10 points)

The upwash experience may save propelling energy as well as reducing resistance.

Write an essay based on the following chart. In your writing, your should (1) interpret the chart, and (2) give your comments. You should write about 150 words on the ANSWER SHEET. (15 points)

Formation flight is more comfortable because passengers cannot see the other planes.

The role that weather plays in formation flight has not yet been clearly defined.

51. You want to contribute to Project Hope by offering financial aid to a child in a remote area. Write a letter to the department concerned, asking them to help find a candidate. You should specify what kind of child you want to help and how you will carry out your plan.Write your letter with no less than 100 words. Write it on ANSWER SHEET 2.Do not sign your name at the end of the letter; use “Li Ming” instead.Do not write the address. (10 points)

Copying Birds May Save Aircraft FuelBoth Boeing and Airbus have trumpeted the efficiency of their newest aircraft, the 787 and A350 respectively. Their clever designs and lightweight composites certainly make a difference. But a group of researchers at Stanford University, led by Ilan Kroo, has suggested that airlines could take a more naturalistic approach to cutting jet-fuel use, and it would not require them to buy new aircraft. The answer, says Dr Kroo, lies with birds. Since 1914, scientists have known that birds flying in formation—a V-shape—expend less energy. The air flowing over a bird’s wings curls upwards behind the wingtips, a phenomenon known as upwash. Other birds flying in the upwash experience reduced drag, and spend less energy propelling themselves. Peter Lissaman, an aeronautics expert who was formerly at Caltech and the University of Southern California, has suggested that a formation of 25 birds might enjoy a range increase of 71%. When applied to aircraft, the principles are not substantially different. Dr Kroo and his team modeled what would happen if three passenger jets departing from Los Angeles, San Francisco and Las Vegas were to assemble over Utah, assume an inverted V-formation, occasionally change places so all could have a turn in the most favourable positions, and proceed to London. They found that the aircraft consumed as much as 15% less fuel (coupled with a reduction in carbon-dioxide output). Nitrogen-oxide emissions during the cruising portions of the flight fell by around a quarter. There are, of course, knots to be worked out. One consideration is safety, or at least the perception of it. Would passengers feel comfortable travelling in companion? Dr Kroo points out that the aircraft could be separated by several nautical miles, and would not be in the intimate groupings favoured by display teams like the Red Arrows. A passenger peering out of the window might not even see the other planes. Whether the separation distances involved would satisfy airtraffic-control regulations is another matter, although a working group at the International Civil Aviation Organisation has included the possibility of formation flying in a blueprint for new operational guidelines. It remains to be seen how weather conditions affect the air flows that make formation flight more efficient. In zones of increased turbulence, the planes’ wakes will decay more quickly and the effect will diminish. Dr Kroo says this is one of the areas his team will investigate further. It might also be hard for airlines to coordinate the departure times and destinations of passenger aircraft in a way that would allow them to gain from formation flight. Cargo aircraft, in contrast, might be easier to reschedule, as might routine military flight.As it happens, America’s armed forces are on the case already. Earlier this year the country’s Defence Advanced Research Projects Agency announced plans to pay Boeing to investigate formation flight, though the programme has yet to begin. There are reports that some military aircraft flew in formation when they were low on fuel during the Second World War, but Dr Lissaman says they are unsubstantiated. “My father was an RAF pilot and my cousin the skipper of a Lancaster lost over Berlin,” he adds. So he should know.

Study the following photos carefully and write an essay of 160~200 words in which you should 1) describe the photos briefly,2) interpret the social phenomenon reflected by them, and3) give your point of view.You should write 160-200 words neatly on ANSWER SHEET (20 points)

Ryan Hooper

Adam Bailey

51. Write a letter to you university library, making suggestions for improving its service.You should write about 100 words on ANSWER SHEET 2.Do not sign your own name at the end of the letter. Use “Li Ming” instead.Do not write address. (10 points)

Aaron Norris

52. Write an essay of 160-200 words based on the following drawing. In your essay, you should1) describe the drawing briefly,2) explain its intended meaning, and then3) support your view with an example/examples.You should write 160-200 words neatly on ANSWER SHEET (20 points)

How seriously should parents take kid’s opinions when searching for a home?In choosing a new home, Camille McClain’s kids have a single demand: a backyard.McClain’s little ones aren’t the only kids who have an opinion when it comes to housing, and in many cases youngsters’ views weigh heavily on parents’ real estate decisions, according to a 2018 Harris Poll survey of more than 2,000 U.S. adults.While more families buck an older-generation proclivity to leave kids in the dark about real estate decisions, realty agents and psychologists have mixed views about the financial, personal and long-term effects kids’ opinions may have.“The idea of involving children in a big decision is a great idea because it can help them feel a sense of control and ownership in what can be an overwhelming process,” said Ryan Hooper, a clinical psychologist in Chicago.“Children may face serious difficulties in coping with significant moves, especially if it removes them from their current school or support system,” he said.Greg Jaroszewski, a real estate brokers with Gagliardo Realty Associates, said he’s not convinced that kids should be involved in selecting a home--but their opinions should be considered in regards to proximity to friends and social activities, if possible.“Younger children should feel like they’re choosing their home--without actually getting a choice in the matter,” said Adam Bailey, a real estate attorney based in New York.“Asking them questions about what they like about the backyard of a potential home will make them feel like they’re being included in the decision-making process,” Bailey said.“Many of the aspects of homebuying aren’t a consideration for children,” said Tracey Hampson, a real estate agent based in Santa Clarita, Calif. And placing too much emphasis on their opinions can ruin a fantastic home purchase.“Speaking with your children before you make a real estate decision is wise,but I wouldn’t base the purchasing decision solely on their opinions.” Hampson said.“The other issue is that many children--especially older ones--may base their real estate knowledge on HGTV shows,” said Aaron Norris of The Norris Group in Riverside, Calif.“They love Chip and Joanna Gaines just as much as the rest of us,” he said.“HGTV has seriously changed how people view real estate. It’s not shelter, it’s a lifestyle. With that mindset change come some serious money consequences. ”“Kids tend to get stuck in the features and the immediate benefits to them personally,” Norris said.“Parents need to remind their children that their needs and desires may change over time,” said Julie Gurner, a real estate analyst with FitSmallBusiness. com.“Their opinions can change tomorrow.” Gurner said.“Harsh as it may be to say, that decision should likely not be made contingent on a child’s opinions, but rather made for them with great consideration into what home can meet their needs best--and give them an opportunity to customize it a bit and make it their own.”This advice is more relevant now than ever before, even as more parents want to embrace the ideas of their children, despite the current housing crunch. remarks that significant moves may pose challenges to children.Ryan Hoopersays that it is wise to leave kids in the dark about real estate decisions.Adam Baileyadvises that home purchases should not be based only on children’s opinions.Tracey Hampsonthinks that children should be given a sense of involvement in homebuying decisions.Aaron Norris[E] notes that aspects like children’s friends and social activities should be considered upon homebuying.Julie Gurner[F] believes that homebuying decisions should be based on children’s needs rather than their opinions. [G] assumes that many children’s views on real estate are influenced by the media.

47. You have just come back from the U.S. as a member of a Sino-American cultural exchange program. Write a letter to your American colleague to1) express your thanks for his/her warm reception;2) welcome him/her to visit China in due course.You should write about 100 words on the ANSWER SHEET.Do not sign your own name at the end of the letter. Use “Zhang Wei” instead.Do not write your address. (10 points)

Andrew Lansley held that