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Attempts until Rnd<constant, has exponential distribution?

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dodo
#1
Aug29-04, 11:31 AM
P: 688
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.
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matt grime
#2
Aug29-04, 11:37 AM
Sci Advisor
HW Helper
P: 9,398
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.
dodo
#3
Aug29-04, 11:58 AM
P: 688
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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