課程名稱︰統計學一上 課程性質︰系必修 課程教師︰羅竹平 開課學院：管理學院 開課系所︰國際企業學系 考試日期（年月日）︰2012/01/10 考試時限（分鐘）：180分鐘 是否需發放獎勵金：是 （如未明確表示，則不予發放） 試題 : 1.(15%)Suppose that you have a random variable X,which has a Bernoulli distribution P(X=1)=p and P(X=0)=1-p.The p is the probability of true. (a)What is the mean and variance? (b)Suppose further that you draw a sample of n observations.What will be the mean and variance of the sample? (c)If the sample portion is k/n,what is the mean and variance of the sample portion? 2.(15%)A survey shows that 60% Taiwanese over 65 years of age oppose use of cell phones when driving a car.If this information is correct and if a research randomly selects 25 Taiwanese who are over 65 years of age. (a)What is the probability that exactly 12 oppose the use of cell phones in driving a car? (b)What is the probability that more than 17 oppose the use of cell phones in driving a car? (c)What is the probability that less than 8 oppose the use of cell phones in driving a car? 3.(15%)A survey shows that households using the Internet in buying or leasing cars reported that 81% were seeking information about prices.In addition,44% were seeking information about products offered.Suppose 75 randomly selected households who are using the Internet in buying or leasing cars are contacted. (a)What is the expected number of households who are seeking price information? (b)What is the expected number of households who are seeking information about product offered? (c)What is the probability that 67 or more households are seeking information about prices? 4.(10%)Suppose that the population of a product has a failure rate of 120 failures per million hours.The product is expected to operate 20000 hours and only 1 failure is expected to occur.What is the possibility? (a)Find out the answer by using Binominal distribution. (b)Find out the answer by using Poisson distribution. 5.(10%)Suppose a random variable X follows the Poisson distribution with -λ x e λ 2 probability as p(X=x)= ────.Please prove that μ=σ =λ.Please also show x! -λ x n! x n-x e λ that lim ───── p (1-p) = ──── (bonus 20%). n→∞ x!(n-x!) x! 6.(15%)In your class with 50 members,two candidates compete for the Class Representative.You conduct a survey from a sample of 16 to know whether your friend will be elected,and find out the sample portion is 52% that he might win.Constuct a 98% confidence interval to estimate that your friend might win. You happen to know that the associate variance is 0.9. 7.(20%)Taiwan is going to have a new president.Suppose there are 12,000,000 qualified voters in Taiwan.Suppose further that,according to historical record,45% of Taiwanese favor the Green party and the remaining the Blue party.A poll before election is conducted.First,please find out the estimated sample size(at least)in your sample poll.Suppose the tolerance of error is 1%. Please conduct a 85% confidence interval to estimate the opportunity of the Green party to win.Suppose that in your survey,the estimated portion of the Green party's votes is 48%. --

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