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108年 - 108年台大土木工程研究所交通組-統計學(C)#123157

科目：研究所、轉學考(插大)◆統計學 | 年份：108年 | 選擇題數：0 | 申論題數：14

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所屬科目：研究所、轉學考(插大)◆統計學

選擇題 (0)

申論題 (14)

1. Show that the mean of a hypergeometric random variable X, the number of successes in a random sample of size n selected from N items of which k are labeled success and N - k labeled failure, is nk/N.
2. The amount of lateral expansion (mils) was determined for a sample of n=9 pulsed-power gas metal arc welds used in LNG ship containment tanks. The resulting sample standard deviation was s=2.81 mils. Assuming normality, derive a 95% confidence intervals for σ².
a. Based on these 100 observations, is a Poisson distribution with a mean of 2.4 an appropriate model? Perform a goodness-of-fit test with α=0.05.
b. Perform the test using P-value approach.
a. Do the data suggest that the two methods provide the same mean value for natural vibration frequency? Using the P-value approach.
b. Find a 95% confidence interval on the mean difference between the two methods and use it to answer the question in part (a).
5. Let X be a random variable with distribution function
 
Plot the graph of F(x) and then evaluate E(x).
6. There are two classes of Probability and Statistics course. The problems of the final exam are identical for the two classes. Let μ₁ and μ₂ denote the population means of scores of class A and class B, respectively, and σ₁ and σ₂ denote the population variances of scores of class A and class B, respectively. A random sample of 13 students are taken from class A and 11 students are taken from class B. The sample average and standard deviation of scores of each class are class A: X̄ₐ = 84, Sₐ = 4 and class B: X̄բ = 77, Sբ = 6. Test whether the population means of scores of the two classes are equal. Make assumptions if necessary.
a. What is the probability function of Y?
b. What is the cumulative distribution function of Y?
c. Find the mean and variance of X.
a. What is the fitted linear regression model?
b. What is the coefficient of determination of this model?
c. Does the model coefficients consistent with the prior knowledge that all three independent variables (x) have positive effect on the dependent variable (y)? Why or why not? Explain your answer.