Attempts until Rnd<constant, has exponential distribution?

1. Aug 29, 2004

dodo

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. Aug 29, 2004

matt grime

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.

3. Aug 29, 2004

dodo

Hmm... Is there an emoticon for embarrasment here? :)