[考古] 機率論/謝新銘/972期中考
[開課學院]:資電學院
[開課系所]:電機系
[課程名稱]:機率論
[老師名稱]:謝新銘老師
[開課學期]:97第二學期
[類型]:97-2期中考
1.An intercom system master station provides music to 3 hospital room.The
probabilty that any one room will be switched on and draw power at any time
is 1/3.When on, a room draws 1W.
(a)Find the probability density function and probability distribution function
for the random variable "power delivered by the master station."
(b)If the master-station amplifier is overloaded when more than 3/2W is daman-
ded, what is its probability of averloaded?
2.A fair coin is tossed twice,and let the random variable X represent the num-
ber of heads.Find the probability density function fX(x) and probability dist-
ribution function FX(x).
3.Suppose that the amount of waiting time a customer spends at restaurant has
an exponential distribution with a mean value of 5 minutes,
fX(x)=1/5exp(-x/5)U(x)
(a)Find the probability distribution function FX(x).
(b)Find the probability that a customer will spend more than 10 mintutes in
the restaurant.
4.Given a random variable X(fi)=10i of fair-die experiment,
(a)find the probability density function fX(x) and probability distribution
function FX(x).
(b)find the expected value (mean) E{X}.
(c)find the conditional probability density function f(x|X>25) and condition-
al distribution function FX(x|X>25).
(d)find the condition expected value (conditional mean) E{X|X>25}.
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