Probability densities

  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. sylas

    sylas 1,734
    Science Advisor

    Not subtract. You have a conditional probability here.
  4. 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. sylas

    sylas 1,734
    Science Advisor

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