首頁 > 線上測驗 > 96-100年研究所統計學歷屆試題(資管、工工、工管)(一年期) > 97年國立成功大學交通管理研究所,電信管理研究所統計學
Let p equal the proportion of college students who favor a new policy for
alcohol consumption on campus. How large a sample is required to
estimate p so that with 90% confidence the maximum error of the
estimate of p is 0.03 when the size of the student body is N = 2000?
(10%)
The six numbers 1, 2, 3, 4, 5, and 6 are written, respectively, on six disks of
the same size and placed in a hat. Two disks are drawn without
replacement from the hat, and the numbers written on them are observed.
(a) List all the possible outcomes for this experiment as pairs of numbers
(order not important). (5%)
(b) If each of the possible outcomes has equal probability, assign a value to
the probability that the sum of the two numbers drawn is (i) 4 and (ii)
between 5 and 7 inclusive. (10%)
You are a member of a class of 20 students. A bowl contains 20 chips, 1
blue and 19 red. Each student is to take 1 chip from the bowl without
replacement. The student who draws the blue chip is guaranteed an A for
the course.
(a) If you have a choice of drawing first, fifth, or last, which position would
you choose? Justify your choice using probability. (2%)
(b) Suppose that the bowl contains 2 blue and 18 red chips. What position
would you now choose? (3%)
Bowl A contains two red chips and two white chips; bowl B contains one
red chip and three white chips; bowl C contains three red chips and one
white chip. A bowl is selected at random (with equal probabilities), and one
chip is taken at random from the bowl.
(a) Compute the probability of selecting a white chip, say P(W) . (5%)
(b) If the chip selected is white, compute the conditional probability that
the other chips in the bowl contain at least one white chip. (10%)
Let X be the smaller outcome when a pair of four-sided dice is rolled.
(a) Find the p.d.f. of X . (5%)
(b) Find the mean, variance, and standard deviation of X . (5%)
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