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Attempts until Rnd<constant, has exponential distribution?

  1. Aug 29, 2004 #1
    Suppose a number U is generated from an uniform distribution [0,1].

    If you repeat the process until U < some constant,
    does the number of loops have an exponential distribution?

    If so, could you point the way to a proof? Thanks in advance.
     
  2. jcsd
  3. Aug 29, 2004 #2

    matt grime

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    no it isn't exponential, but this looks like homework, and is quite easy: write down the probability that the first pick less than, say, p occurs on the k'th turn and note which distribution you get.
     
  4. Aug 29, 2004 #3
    Hmm... Is there an emoticon for embarrasment here? :)

    (google-google-google...)
    http://mathworld.wolfram.com/GeometricDistribution.html (for attempts-1, i.e., failures until success)

    Guess I only needed a little tap on the head to remove the spiderwebs.
    Thank you!
     
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