电大应用概率统计复习试题资料.doc

学生姓名：学号：专业年级：成绩：一、 填空题（每小题2分，本题共16分）1、设随机变量，则。 （ 已知标准正态分布函数值：）2、设随机变量服从泊松分布且具有方差2，那么的分布律为 。3、设一维连续型随机变量的概率密度函数为，则随机变量的概率密度函数为 。4、以下是利用MINITAB对变量和的线性相关性作回归分析所得结果，由此判定回归 方程是 。The regression equation isy = 0.63 + 0.040 xAnalysis of VarianceSource DF SS MS F PRegression 1 0.178 0.178 0.13 0.725Residual Error 9 12.200 1.356Total 10 12.3785、设总体是它的一个样本，则 服从 分布。6、设正态总体的均方差，该总体的一个容量为的样本的样本均值，则 总体均值的置信水平为95%的置信区间是 。7、在双因素有交互作用的方差分析中，设因素有3个水平，因素有2个水平，每个 处理作两次重复试验，则试验误差平方和的自由度 。8、设关于的线性回归方程为，则。 （ ）二、单项选择题（每小题2分，本题共18分）1、设则。 2、设是相互独立的两个随机变量，则。3、二维随机变量的分布函数。 4、多个相互独立的服从正态分布的随机变量的线性组合服从。二项分布 泊松分布 均匀分布 正态分布 5、以下哪一个MINITAB命令用于作回归分析。 6、以下哪一个MATLAB命令用于求定积分。 7、设总体，对检验水平，欲检验方差由容量为的一个样本计算出来的统计量的观察值应与作比较。 8、参数的点估计量的无偏性指的是。 9、设是总体的一个样本，则总体方差的矩法估计量是。 三、计算题（每小题8分，本题共56分）1、在次品率为5%的一批产品中任取5件，求其中至少有两件次品的概率。2、以下是某农作物对三种土壤，四种肥料，每一个处理作三次重复试验后所得产量的方差分析表的部分数据，完成方差分析表并写出分析结果。方差来源平方和自由度均方和值临界值土壤因素肥料因素误差总和（参考临界值：）3、某工厂生产的一种电子设备的寿命（以1000小时为单位）服从以为参数的指数分布。设产品的单位成本是200元，售价是500元。但是，如果，则工厂承担全部退款。试求工厂承担全部退款的概率以及一件产品的期望利润。4、某工厂生产的某种产品的合格率为92%，假定质检系统是经过简化的，对合格品以96%的概率给出合格的结果，对不合格品同样以96%的概率给出不合格的结果。试求产品经质检后为合格品的概率，又问一件经检验为合格品的产品确是合格品的概率是多少？ 5、假定某种电池的工作时间服从正态分布，观察五个电池的工作时间（小时）为： 32，41，42，49，53问这批样本是否取自均值为50（小时）的总体？（） （）6、设二维随机变量的联合概率密度函数如下，试求，并问与是否相互独立？7、已知随机变量的概率密度函数为，求的分布函数 及事件的概率。四、综合实验（本题10分，开卷，解答另附于数学实验报告中）华南农业大学期末考试试卷（A卷）2003学年 第二学期考试科目：应用概率统计（答案）评卷人：学生姓名：学号：专业年级：成绩：一、 填空题（每小题2分，本题共16分）1、设随机变量，则。 （ 已知标准正态分布函数值：）2、设随机变量服从泊松分布且具有方差2，那么的分布律为。3、设一维连续型随机变量的概率密度函数为，则随机变量的概率密度函数为 。4、以下是利用MINITAB对变量和的线性相关性作回归分析所得结果，由此判定回归 方程是 无效的 。The regression equation isy = 0.63 + 0.040 xAnalysis of VarianceSource DF SS MS F PRegression 1 0.178 0.178 0.13 0.725Residual Error 9 12.200 1.356Total 10 12.3785、设总体是它的一个样本，则 服从分布。6、设正态总体的均方差，该总体的一个容量为的样本的样本均值，则 总体均值的置信水平为95%的置信区间是或 。7、在双因素有交互作用的方差分析中，设因素有3个水平，因素有2个水平，每个 处理重复两次试验，则试验误差平方和的自由度 6 。8、设关于的线性回归方程为，则。 （ ）二、单项选择题（每小题2分，本题共18分）1、设则。 2、设是相互独立的两个随机变量，则。3、二维随机变量的分布函数。 4、多个相互独立的服从正态分布的随机变量的线性组合服从。二项分布 泊松分布 均匀分布 正态分布 5、以下哪一个MINITAB命令用于作回归分析。 6、以下哪一个MATLAB命令用于求定积分。 7、设总体，对检验水平，欲检验方差由容量为的一个样本计算出来的统计量的观察值应与作比较。 8、参数的点估计量的无偏性指的是。 9、设是总体的一个样本，则总体方差的矩法估计量是。 三、计算题（每小题8分，本题共56分）1、在次品率为5%的一批产品中任取5件，求其中至少有两件次品的概率。解：设表示5件产品中次品的数目，则 （2分）所求的概率为 （3分） （2分） （1分）2、以下是某农作物对三种土壤，四种肥料，每一个处理作三次重复试验后所得产量的方差分析表的部分数据，完成方差分析表并写出分析结果。方差来源平方和自由度均方和值临界值土壤因素214.360.28肥料因素3186.993.71614.780.29误差2450.44总和35（参考临界值： ）（表格：5分）分析结果：因为， 所以因素，即肥料对农作物产量的影响是有统计意义的，而因素，即土壤对农作物的产量的影响没有统计意义，肥料和土壤之间也不存在交互效应。 （3分）3、某工厂生产的一种电子设备的寿命（以1000小时为单位）服从以为参数的指数分布。设产品的单位成本是200元，售价是500元。但是，如果，则工厂承担全部退款。试求工厂要承担全部退款的概率及一件产品的期望利润。解： （4分） 令表示一件产品的利润，则的分布律为：（分布律：2分）一件产品的期望利润（元） （4分）4、某工厂生产的某种产品的合格率为92%，假定质检系统是经过简化的，对合格品以96%的概率给出合格的结果，对不合格品同样以96%的概率给出不合格的结果。试求产品经质检后为合格品的概率，又问一件经检验为合格品的产品确是合格品的概率是多少？解：设A 表示任取的一件产品是合格品，B表示任取的一件产品被检验为合格品。 则产品经质检后为合格品的概率： （4分） 一件经检验为合格品的产品确是合格品的概率为： （4分）5、假定某种电池的工作时间服从正态分布，观察五个电池的工作时间（小时）为： 32，41，42，49，53问这批样本是否取自均值为50（小时）的总体？（） （）解法一：已知 检验假设： （2分）因为总体方差未知，所以用T统计量作检验： （2分）由样本计算得的观察值为： （2分）所以接受假设，可以认为这批样本是取自均值为50（小时）的总体。 （2分）解法二：已知 检验假设： （2分）因为总体方差未知，所以用T统计量作检验： （2分）由样本计算得的观察值为： （2分）所以接受假设，可以认为这批样本是取自均值为50（小时）的总体。 （2分）6、设二维随机变量的联合概率密度函数如下，试求，并问与是否相互独立？解：（1） （2分） （2） （2分） （2分）显然, ;所以，x 与 y 非相互独立。 （2分）7、已知随机变量的概率密度函数为，求的分布函数 及事件的概率。解：（1）当时， 当时， 当时， 综上所述， （4分） （2） （2分） （2分）四、综合实验（本题10分，开卷，解答另附于数学实验报告中）Visa-free policy brings Chengdu biz, tourism boost. Making national headlines several times, Chengdu's 72-hour visa-free policy has attracted wide attention from both Chinese and foreign experts and businessmen since it took effect on Sept 1 last year. The program permits citizens from 51 countries and regions including the United States, Australia, Canada and Japan who have valid visas and flight tickets to a third country to spend three days in the city. The capital of Sichuan province is the first city in the western region of China to offer foreign tourists a three-day visa and the fourth nationwide to adopt the policy following Shanghai, Beijing and Guangzhou. Li Zhiyong, deputy dean of the tourism institute at Sichuan University, said the move "contributes to a large increase in the number of overseas tourists and raises the city's level of internationalization". "The policy will also bring direct economic revenue," Li said. "Chengdu has many cultural legacies and is also a paradise for panda lovers with the world's largest breeding and research center. Three days are long enough for foreign visitors to visit those iconic tourist spots," he noted. The city is home to the remains of the Jin sha civilization that dates back more than 3,000 years as well as the Qing cheng Mountains and the Du jiang yan irrigation system. Qing cheng has long been recognized as the birthplace of Taoism, China's ancient indigenous religion, while Du jiang yan is considered to be the oldest functioning water-control project in the world. Chengdu ranked third in tourist facilities, management and services among 60 Chinese cities in a customer satisfaction survey released last year. But, Li added that efforts are still needed to develop more tourism products, improve English services and provide accurate translation of traffic signs and scenic billboards. Zhao Yun, chairwoman of British Chamber of Commerce Southwest China, told China Daily that his colleagues found the policy very convenient. "A British client once flew here and stayed for just one day to check her ordered goods," she said. Zhao was born in Shanxi province, but she has lived in Chengdu for more than 10 years. "My life was like a running race moving from place to place. I also lived in Beijing and Shanghai before," she said. "But Chengdu is a place that you never want to leave once settling down. It is now my second hometown," she said. If the environment is further improved, the city will attract more people to visit and live, with the 72-hour visa-free policy and compelling conditions in transportation, culture, climate and cuisine, he said. Foreigners also gave positive feedback on the policy. A spokesman from Dell Inc said the company has a global hub of operation in Chengdu, so the three-day visa "has an immediate and positive influence on the company's business development". Rudy Buttignol, president of the public broadcasting company in British Columbia, Canada, said his work requires frequent travel to Chengdu and the policy "makes the trips easier". Data from the city's public security bureau shows some 100 foreign visitors enjoyed the 72-hour policy by the end of March, most of them from the United States, the United Kingdom and Germany. Chengdu also reported robust growth in its overall tourist industry last year. Official statistics show that it received some 150 million tourists last year, an increase of 28 percent from 2012. Around 1.7 million came from abroad, an increase of 12 percent. Total revenue from tourism surpassed 133 billion yuan ($21.7billion). During his visit to Kazakhstan in September, Chinese President Xi Jinping proposed that China and Central Asia join hands to build a Silk Road economic belt to boost cooperation. The idea has been widely echoed in Central Asian countries, becoming an encouraging blueprint for Chinese areas along the Silk Road that has linked Asia and Europe for more than 2,000 years. In the next three weeks, China Daily reporters will travel through the belt in China and in Kazakhstan, Uzbekistan and Turkey. They will show the progress and expectations of the countries, businesses and peoples on the route. Shaanxi - the start of the ancient Silk Road - has positioned itself as the new starting point for the development of the Silk Road Economic Belt, which will strengthen China's cooperation with Central Asian countries, a senior official said. Shaanxi Governor Lou Qinjian said the province is fresh, rich and unique, as it was when it anchored one end of the ancient Silk Road. "It is the best option for accommodating industrial transfers from East China or the world at large," he said on Wednesday in Xi'an.Lou held a joint interview with 27 media, including China Daily, the first in a series of interviews entitled Chinese Media Along the Silk Road. The interviews will be in Shaanxi and Gansu provinces and the Xinjiang Uygur autonomous region, as well as Kazakhstan, Uzbekistan and Turkey.The media group held the first interview on Wednesday morning in Xi'an, the starting point of the ancient Silk Road, a trade channel established more than 2,000 years ago linking China, Central Asia and Europe.10