若某路口每月(以30天计)发生车祸之次数为波以松分布.doc

八十九學年度第二學期統計學(二) Mid-term Exam (C卷)20/01/27一、 Multiple Choice and True/False (9%, 3% each):1. If the mean and variance for the population are 900 and 9 respectively, what are the mean and variance of the sample mean if the sample size is 16?a. 900, 144b. 900, 0.5625c. 900, 1296d. 900, 92. A random sample of size 100 is drawn from a binomial distribution with mean 32 and variance 16. What is the distribution of ?a. Normal with mean 32 and variance 1.6b. Normal with mean 0 and variance 1c. Binomial with n = 64 and p = 0.5d. None of the above3. X is distributed with m = 10 and s2 = 4. Y is distributed with m = 50 and s2 = 100. Which one has higher coefficient of variation?a. Xb. Yc. the samed. couldnt tell二、 Short Answer: (21%)1. (6%) 若某路口每月（以30天計）發生車禍之次數為波以松分布，平均次數為6 次，則該路口發生車禍之間隔時間為_分布，平均間隔時間為_天。2. (3%) List the formula for Chebyshevs Inequality: 3. (3%) If sample mean = 100, sample standard deviation = 10, and sample size = 16, what is the stand error of the sample mean?_4. (6%) 某電子公司生產一產品，該產品之電阻值呈常態分布(m = 100W, s = 10W)a. 試問該產品一批(10,000個)，約有多少個超過120W？_b. 隨機抽樣25個，其平均電阻值小於96W之機率為多少？_5. (3%) A random sample of 36 observations has been drawn from a normal distribution with mean 50 and standard deviation 12. The probability that the sample mean is in the interval 47, 53 is _.三、 Open Question: (70%)1. (15%) Assume that one has 2 independent random samples of sizes n1, n2 from the same population. Show that is a better estimator for m than .2. (15%) 請說明: a. 中央極限定理; b. 大數法則; c. 常態分布之標準化。3. (10%) Let X be a random variable with the following probability distribution:Find the maximum likelihood estimator of a, based on a random sample of size n.4. (15%) The following data are the temperatures of effluent at discharge from a sewage treatment facility on consecutive days:434751485250464945524651444946514945445048504950a. Calculate the sample mean and sample variance.b. Construct a stem-and-leaf plot of the data.c. Construct a box plot of the data and comment on the information in this