課程名稱︰統計學一上 課程性質︰必修 課程教師︰王衍智 開課學院：管理學院 開課系所︰財務金融學系 考試日期（年月日）︰101.11.21 / 11.28 / 12.05 / 12.19 考試時限（分鐘）：15/10/10/15 是否需發放獎勵金：是 （如未明確表示，則不予發放） 試題 : Statistics I Quiz 3 Date: 21 Nov 2012 Time: 9:10-9:25. 1. A joint probability chart is shown below: (30%): Y=1 Y=2 Y=3 Y=4 X=1 0.1 0 0 0 X=2 0.2 0.05 0.15 0 X=3 0.15 0.05 0.1 0.2 a) Please write fX|Y(X=a|Y=b). b) Please find E(X|Y) c) Please find E(X*Y0.5|Y) 2. A census suggests 0.5% of man get liver cancer at their 40. If Mr. White in his 40 gets screened for liver cancer and receives a positive test result. The medical examination he did has error for 1 positive test out of 1000 healthy people and for 10 negative tests out of 1000 people with liver cancer. What is the probability that he does have liver cancer? (30%) 3. A lottery has 20% of rate to draw a prize. Find the probability of winning twice out of buying 8 lotteries. (20%) ----------------------------------------------------------------------- Statistics I Quiz 4 Date: 28 Nov 2012 Time: 9:10-9:20. 10 5 1.Let Z~N(0,1). W=ΣZ^2 and V=ΣZ^2. X=W/2V. i=1 i=1 Please answer following questions: (i) What are population mean and variance for W and V (40%). (ii) What is population mean for X. 2. You randomly sample 5 i.i.d. random variables X1-X5 from a population 5 3 (mean μ and σ2). For two statistics W and V for, W=(Σ Xi)/5, V=(Σ Xi)/3. i=1 i=1 Please answer following questions (40%). (i) Show that W and V are all unbiased estimators. (ii) Show that W is more efficient than V. 3. [True or false, please explain if you think the state false]: A consistent estimator is always an unbiased estimator (20%). -------------------------------------------------------------------- Statistics I Quiz 5 Date: 5 Dec 2012 Time: 9:10-9:20. 1. The mean GPA of 100 students is 76 and the population standard deviation σ= 10. Please find: i) Critical value Z* at 95 confidence level. ii) Margin of error under 95% confidence levels. iii) A 95% confidence interval for mean GPA. iv) Now we are willing to settle for margin of error 1.0 next year. How many students should we survey? 標準常態機率表:http://imgur.com/kE59cdq ------------------------------------------------------------------------ Statistics I Quiz 6 Date: 19 Dec 2012 Time: 9:10-9:25. 1. Researcher wants to know if price appreciates and samples 9 observations. Test of hypothesis at 5% significance level (α) at one-tail for changes in prices (π) is examined: H0: μπ= 0 versus Ha: μπ> 0. Please answer following questions: ─ i) If average of nine samples (π) is 0.5, and population SD (σπ) is 5. Please show the sample mean is statistically significant or not (assume population SD is known). ii) If true mean of changes in prices π is 1 and null hypothesis is wrong, please find the power under μπ=1 (assume population SD is known). iii)Find probability of type II error from previous question. iv) Now we assume population SD is unknown, and we get sample SD (sπ) equal to 5. If true mean of changes in prices π is 1.253 and null hypothesis is wrong, please find the power under μπ=1. 標準常態機率表:http://imgur.com/kE59cdq T分配臨界值表:http://imgur.com/F0AjaP5 --

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