## Attempts until Rnd<constant, has exponential distribution?

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.
 PhysOrg.com science news on PhysOrg.com >> King Richard III found in 'untidy lozenge-shaped grave'>> Google Drive sports new view and scan enhancements>> Researcher admits mistakes in stem cell study
 Recognitions: Homework Help Science Advisor 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.
 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!