[开课学院]:资电学院 [开课系所]:电机系 [课程名称]:机率论 [老师名称]:谢新铭老师 [开课学期]:97第二学期 [类型]: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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