課程名稱︰工程統計學
課程性質︰必修
課程教師︰周家蓓
開課學院：工學院
開課系所︰土木工程學系
考試日期（年月日）︰中華民國九十八年十一月十日
考試時限（分鐘）：110分鐘
是否需發放獎勵金：是
（如未明確表示，則不予發放）
試題 :
工程統計學(02班)期中考試題 2009/11/10
1. (15%) In the senior year of a high school graduating class of 100 students,
42 studied mathematics, 68 studied psychology, 54 studied history, 22
studied both of mathematics and psychology, 7 studied history but neither
mathematics nor psychology, 10 studied all three subjects, and 8 did take
any of the three. If a student is selected at random, find the probability
that
(a) a person enrolled in psychology takes all three subjects;
(b) a person not taking psychology is taking both history and mathematics.
2. (15%) A real estate agent has 8 master keys to open several new homes. Only
1 master key will open any given house. If 40% of these homes are usually
left unlocked, what is the probability that the real estate agent can get
into a specific home if the agent selects 3 master keys at random before
leaving the office?
3. (15%) The proportion of people who respond to a certain mail-order
solicitation is a continuous random variable X that has the density
function
/ [2(x+2)]/5 , 0 < x < 1
f(x) =
\ 0 , elsewhere.
(a) Show that P( 0 < X < 1) = 1.
(b) Find the probability that more than 1/4 but fewer than 1/2 of the
people contacted will respond to this type of solicitation.
4. (10%) Proof the variance of a random variable X is
σ^2 = E(X^2) - μ^2
5. (20%) Suppose that hte building code for the design of buildings in a
coastal region specfies the 50-yr wind as the "design wind." That is, a
wind velocity with a return period of 50 years; or on the average, the
design wind may be expected to occur once every 50 years. Find the
probability that
(a) a newly completed building in the region will be subjected to the
design wind velocity for the first time on the fifth year after its
completion?
(b) the first such wind velocity will occur within 5 years after completion
of the building?
(c) the building in the region will be subjected to the design wind for the
third time on the tenth year?
(d) the third design wind will occur within 5 years?
6. (15%) A major steel pipeline is used to transport crude oil from an oil
production platform to a refinery over a distance of 10 km. Even though the
pipeline is inspected once a year and repaired as necessary, the steel
material is subject to damaging corrosion. Assume that from past inspection
records, the average distance between locations of such corrosions is
determined to be 0.15 km. In this case, if the occurence of corrosions
along the pipeline is medeled as a Poisson process with a mean occurrence
rate of v=0.15/km, what is the probability that
(a) there will be 10 locations of damaging corrosion between inspections?
(b) at least five corrosion sites between inspections?
7. (10%) Please describe the difference between "independent" and "mutually
exclusive" of two events.
(以下空白)
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