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Probability densities

  1. Dec 13, 2009 #1
    Heres the question.... The time between arrivals of taxis at a busy intersection is exponentially distributed with a mean of 10 minutes.

    The question I am stuck on is....

    Suppose you have already been waiting for one hour for a taxi, what is the probability that one arrives within the next 10 minutes. (The first part of the problem was to find probability you wait longer then an hour which I figured the limits would be (60<x<infinity).

    Well i know mew=beta=10 min=1/lambda=1/10

    f(x)= lambda*e^-lambda which will ultimately give me 1/10e^-1/10xdx. I have my integral set up, the thing is I cant figure out my limits. My initial guess was to evaluate the integral from (0<x<60) and subtract (70<x<infinity), ultimately giving me the answer .9984 or 99.84%. I thought it was right but apparently wrong, can someone please help me set up the appropriate limits. Thanks in advance.
  2. jcsd
  3. Dec 13, 2009 #2


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    Not subtract. You have a conditional probability here.
  4. Dec 13, 2009 #3
    Ok so if my given is the answer I got for my first part, .0025. How would I go on finding the Probability of P(AintersectB)?
  5. Dec 13, 2009 #4


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    You need Pr(60 < t < 70) given Pr(60 < t). What's the formula for that?
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