田堯章 工統期中考考古題
1.the joint density function of two random variables X and Y is
f(x,y)=2 0<x<y 0<y<1
=0 elsewhere
a. determine if X and Y are independent
b. find Pr(1/4<x<1/2 | Y=2/3)
c. find Pr(X>1/2)
d. find Pr(X>1/2|Y=2/3)
2.the joint density function of two random variables X and Y is given as
X
f(x,y) 1 2 3
4 0.05 0.35 0.00
Y 5 0.00 0.10 0.10
6 0.20 0.05 0.15
a. are X and Y statistically independent?
b. is X more"variable"than Y?
c. are X and Y statically uncorrelated?
(必須詳述理由與過程)
3. the return period of an earthquake with magnitude 7 in Central Taiwan
is 100 years .
a.Determine the probability that this region will have one or two earthquake
of this magnitude in the next 50 years(design life of a new structure)
b.if the service life of an old structure is 20 years,what is the probability
that this structure will esperience the earthquake of magnitude 7?
4. A manufacturer of concrete claims that the strength of his producte is ,on
the average ,4000 psi with atndard deviation of 300 psi. assume that the
strength follows a normal distribution Six sample are selected and tested .
a. find the probability that the sample standard deviation is less than
212.5 psi
b.Determine the probability that the sample mean is between 3900psi and
4200psi.
5.the tensile strength of a certain metal component is normally distributed
with a mean 100ksi and a standard deviation of 1ksi Measurements are recorded
to the nearest 0.5ksi
a.what proportion of these components exceed 101.5ksi in tensile strength?
b.find the probability tha among next 1000 testing samples,at least 42 samples
will have the tensile strength exceeding 101.5ksi.
--
音樂聲盤旋四方........ 我ㄉ心是白鴿隨著風放追遠方.
帶著音符和等待遇上喜雀ㄉ心情...告訴我在遙遠彩虹ㄉ無界.
凝聚著一雙少女ㄉ眼....滿載熱情溢散ㄉ氣息.
攜我回到清淨無為ㄉ遠盡.......
--
※ 發信站: 批踢踢實業坊(ptt.twbbs.org)
◆ From: oar.m6.ntu.edu.tw