国际教育学院2008年12月考试试题.doc

武汉理工大学考试试题纸（ A 卷）课程名称 概率论与数理统计 专业班级 国际教育学院07级本科 题号一二三四五六七八九十总分题分301010810101210备注: 学生不得在试题纸上答题(含填空题、选择题等客观题) ,=2.6025, =2.58351. Fill in the blanks. (310)(1) A pair of dice are tossed. The probability of getting a total of 5 is . (2) Suppose A and B are independent events, and P(A) = 0.3 and P(A+B) = 0.8. Then P(B) = .(3) One person shot at a target independently 4 times. Suppose the probability that at least one time he hit the target is 80/81. Then the probability that he hits the target at one time is . (4) Suppose that X N(1,4), and The value of C is .(5) Given that Cov(X,Y)=, then Cov(2X,-6Y)= .(6) X1, X2, X3 is a random sample from a population N(0,1), then .(7) Suppose that that X1, X2, , Xn form a random sample of the distribution N(). Then .(8) is a random sample from population. If is a unbiased estimator of, then .(9) Randomly select a sample of size 36 from the distribution . Then the probability of that is between 4 and 6 is .(10) Suppose that X1, X2, , Xn are a random smaple from population Xand are unknown. The confidence interval for with confidence coefficient is .2.(110) In a city, 50.2 percent of the people are men and 49.8 percent of the people are women. Records show that the probability that a man has a certain disease is 0.05 and the probability that a woman has the disease is 0.01. If a person in the city is selected at random and is found to have the disease, what is the probability that the person is a woman? 3. (110) Suppose that XU(0, 1). Determine the p.d.f. of the random variable .4. (110) Suppose that the p.d.f. of a random variable X is as follows:(1) Find the value of the constant A; (2) Find the distribution function F(x) of X;(3) Find the values of P(0.1x0.7).5. (110) Suppose the joint distribution of (X,Y) is Y X01200.250.10.310.150.150.05(1) Find the marginal probability distributions of X and Y .(2) Determine whether or not X and Y are independent.(3) Determine the distribution of Z=X+Y .6. (110) On a test paper, there are 48 selective questions and each one has 4 spare answers of which only one is correct. If a correct answer is chosen, you can get 1 score, you get 0 if a wrong answer is chosen. Suppose that you just chose all the answers randomly, and chose one answer for each question. Determine the probability that you can get more than 18 scores. (Use the Central Limit Theorems)7. (110) Suppose that that X1, X2, , Xn are a random sample from population X for which the p.d.f. is where the parameter is unknown and that x1, x2, , , xn are observed values of X1, X2, ,Xn. (1) Determine the moment estimators of . (2) Determine the maximum likelihood estimator of .8. (110) Suppose that weights, in kilograms, of bags of dextrose packed by a machine have a normal distribution for which the mean is unknown and the variance and that the average weight is 0.5kg when the machine work normally. Suppose that one day 9 bags of dextrose are selected at random in order to inspect whether the machine work normally and the average weights of these 9 bags of dextrose is 0.5112kg.Given a level of significance , determine whether the machine worked normally on that day.武汉理工大学教务处 试题标准答案及评分标准用纸 课程名称 概率论与数理统计 （ A 卷）1. (310) (1) 1/9 ； (2) 5/7 ； (3) 2/3 ； (4) 1 ； (5) 1/2；(6) ；(7) ； (8)2006/2007 ；（9）0.8664 ； (10) 2. Let A be the event that the selected person is a man. B be the event that the selected person has the disease.Then; .2Thus the desired probability is 1) . 42) P()= . 4 3. The p.d.f. of X is 2Since as 0x1, thus if , ; .2If , then FY (y)=, we have Thus, t