Attempts until Rnd<constant, has exponential distribution?by dodo Tags: attempts, distribution, exponential, rnd<constant 

#1
Aug2904, 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. 



#2
Aug2904, 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.




#3
Aug2904, 11:58 AM

P: 688

Hmm... Is there an emoticon for embarrasment here? :)
(googlegooglegoogle...) http://mathworld.wolfram.com/GeometricDistribution.html (for attempts1, 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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