99年國立成功大學工業與資訊管理學系統計學線上測驗

1.: For the three distributions, Poisson, Exponential(Exp), and Gamma, one and only
one of the following statements is correct. Which one? (5%)
(A): the expected values of Poisson and Exponential distributions are the same.
(B)
(C): The standard deviation of Poisson distribution is equal to the expected value of
Poisson distribution.
(D): The exponential distribution is often referred to the number of occurrences of
an event over a specified interval of time.

2.
(A): DEBAC
(B): EDABC
(C): BCAED
(D): CDEBA

3.: Three machines A , B and C produce respectively 60%, 30%, and 10% of the
total number of items of a factory. From previous record, the percentages of the
defective output of these machines are 2%, 3%, and 4%, respectively. Suppose an
item is selected at random and is found defective. What is the probability that the
item was produced by machine A ? (10%)

4.: An electrical firm manufactures a product that has a life time that is normally
distributed with a mean of 800 hours and a standard deviation of 40 hours. For the
quantity of 1,000 in this product, how many will have life times between 778 and
834 hours? (14%)

5.: An estimator can be defined as a rule that tells how to calculate the value of an
estimate based on the measurement contained in a sample. We often want to use an
unbiased estimator for a point estimation, what exactly the meaning of “nubiased”?
Please explain it by example without equations. (16%)

6.

7.

Six leaves of some kind of plant are collected from each one of five different locations.
The mean and standard deviation of the length of the leaves are summarized in the
following table. The ANOVA will be used to determine whether the mean lengths of

the leaves from different locations are significantly different under a 95% confidence
level.

(一) Formulate the null hypothesis. (2%)
(二) What are the necessary assumptions for this hypothesis testing? (6%)
(三) Construct the ANOVA table. (6%)

8.

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