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1、型特殊分配1. T 悬指数分数，PT W2 = 2 PT>4,就曲 VarT =。2. Suppose that life of a certain type of electronic component has an exponential distribution with a mean life of 600 hours. Considerthe situation that the component has been in operation for 400 hours. Please find out the conditional probability that it
2、will last for another 600 hours.3. Suppose that the amount of time that a lightbulb works before burning itself out is exponentially distributed with mean eight hours. Suppose that Peggy enters a room in which a lighbulb is burning. She desires to work for five hours. The probability that she will b
3、e able to complete herwork without the bulb burning out is.4. The college of management at National Chung Cheng University requires a minimum test score of 26. The test score among high school seniors in a given school district is normally distributed with mean 22 and standard deviation 2. The perce
4、ntage of high school seniors who are potential recruits is.5. Exhibit 2The expectancy of a particular brand of tire is normally distributed with a mean of 40,000 and standard deviation of 5,000 miles.(1) Refer to Exhibit 2.What is the probability that a randomly selected tire will have a life of at
5、least 30,000 miles?(A)0.4772(B)0.9772(C)0.0228(D)0.5000(2) Refer to Exhibit 2.What is percentage of tires will have a life of 34,000 to 46,000 mils?(A)38.49%(B)76.98%(C)50%(D)88.49%(3) Refer to Exhibit 2.What is the probability that a randomly selected tire will have a life of exactly 47,500 miles?(
6、A)0.0000(B)0.9332(C)0.0668(D)0.49936. To describe distribution of the characteristics of the data collected, we may use the so-called empirical rule (i.e. approaching a normal distribution) and Bienayme-Chebyshev Rule. Ifthe average and the standard deviation of the score of statistical course are 7
7、6 and 7. determine if the following two data 98 and 58 are outlies? (None： It is defined that a datum is regarded as an outliers if the probability of occurrence is less than 1%)7. Suppose 40% of all college students have a computer at home and a sample of 64 taken. What is the probability that more
8、 than 30 of those in the sample have a computer at home?(A)0.3686(B)0.1314(C)0.8686(D)0.6314 (E)None of the above.8. ISY的随械建数，其械率密度函数:?e% , P >0 , 0Wy<8 f (y产(P、0,其他IS求：(1)P(Y >a+b ),其中 a >0、b >0O(2)修件械率P(Y>a+b|Y>a.9. Suppose that YjIlYi are i.i.d. random variables with N 1,4 di
9、stribution.Then the probability density of Y when n=2 and when n = 10 is(A) the same(B) different(C) not comparable(D) None of the above answers are correct.10. If Y has an exponential distribution, show that PY_t T|Y_T =PY_t .11. A grapefruit juice producer buys all his grapefruits from a large gra
10、pefruit grove. The amount of juice squeezed from each of these grapefruits is approximately normally distributed with a mean of 10.0 ounces and a standard deviation of 1.0 ounce.(1) What is the probability that a randomly selected grapefruit will contain between 9.5 and 11.00 ounW(2) 80% of the grap
11、efruits will contain at least how many ounces of jui(e?(3) If random samples of 20 grapefruits are selected, what is the probability that the sample mean would be between 9.5 and 11.0 ounce(4) Suppose the population mean and standard deviation of the amount of juice squeezed from the grapefruits are
12、 unknown, and a sample of 6 grapefruits is selected from the population. The amounts of juice squeezed from those 6 grapefruits are 9.1, 10.1,9.3, 9.1,9.8, and 9.6 ounces. Construct the 95% confidence interval for the population mean.12. Let X be uniformly distributed between a and b and symmetric a
13、bout zero with variance 1. What is the value of a2 +b2 ?(A) 2(B) 4(C) 6(D) 8(E) 1013.某公司各:»£品每月金肖售量都呈垣常憩分配。Aj£品的常憩分配是N (100,300), Bjg品的常!分配是N (80,200), Cjg品的常ig分配是N (120,400 ),各品的金肖售量彼此不曾互相影簪，亦即三者相互3蜀立,者青的：(1)公司每月平均金肖售量悬何？(2)公司每月金肖售量的襟型差悬何？(3)每月金肖售量低於270的械率悬何？14. Suppose x is a random
14、 variable best described by uniform probability distribution with c = 20 and d = 45 .(1) Find f x(2) Find the mean and standard deviation of x.(3) Graph f x . and locate 口 and the interval二 2。on the graph.15. Electronic components of a certain type have a length of lifeY with probability density giv
15、en by：f x = 1100e",y 0,otherwise(1) Suppose that two such components operate independently and in series in a certain system (that is, the system fails when either component fails). Find the density function for X , the length of life of the system.(2) Suppose that two such components operate in parallel (that is, the system does not fail until both components fail). Find density function foX , the length of lift of the system.