Statistical Sciences 2141A/B Lecture Notes - Lecture 17: Exponential Distribution, Random Variable, Memorylessness
23 Oct 2018
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An exponential random variable x is an rv that is often used to model failure or waiting times and interarrival times. It has a state space x 0. The para(cid:373)eter of the distri(cid:271)utio(cid:374) is where > 0. The pdf and cdf of the exponential distribution are. Using integration by parts it can be shown that. Therefore, the variance of the exponential distribution is. The 100pth percentile is the value of x such that p = f(x) Time headway in traffic flow is the elapsed time between the time that one car finishes passing a fixed point and the time that the next car begins to pass that point. Let x be the time headway in seconds for two randomly chosen consecutive cars on a freeway during a period of heavy flow with pdf supposing there is no density associated with times less than 0. 5 seconds. Find the probability that the headway is at most 5 seconds.
