How many draws of a random number [0,1] are needed to sum to 1
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How many draws of a random number [0,1] are needed to sum to 1
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Re: How many draws of a random number [0,1] are needed to sum to 1
#2Isn't the pdf of a uniform distribution just f(x) = 1. What he gave was an exponential distribution with rate parameter lambda. The rest of the math seems correct. But the dependence on e is not surprising as it is relevant to the initial pdf. Am I missing something?
Re: How many draws of a random number [0,1] are needed to sum to 1
#3Interesting, but I hope he's read all those books and isn't just listing any he's found...
Re: How many draws of a random number [0,1] are needed to sum to 1
#4Isn't the pdf of a uniform distribution just f(x) = 1. What he gave was an exponential distribution with rate parameter lambda. The rest of the math seems correct. But the dependence on e is not surprising as it is relevant to the initial pdf. Am I missing something?
[deleted]
Re: How many draws of a random number [0,1] are needed to sum to 1
#5Isn't the pdf of a uniform distribution just f(x) = 1. What he gave was an exponential distribution with rate parameter lambda. The rest of the math seems correct. But the dependence on e is not surprising as it is relevant to the initial pdf. Am I missing something?
It's very easy to verify experimentally that e is likely the correct answer.
Re: How many draws of a random number [0,1] are needed to sum to 1
#6Isn't the pdf of a uniform distribution just f(x) = 1. What he gave was an exponential distribution with rate parameter lambda. The rest of the math seems correct. But the dependence on e is not surprising as it is relevant to the initial pdf. Am I missing something?
You are correct.
Re: How many draws of a random number [0,1] are needed to sum to 1
#7Isn't the pdf of a uniform distribution just f(x) = 1. What he gave was an exponential distribution with rate parameter lambda. The rest of the math seems correct. But the dependence on e is not surprising as it is relevant to the initial pdf. Am I missing something?
It's very easy to verify experimentally that e is likely the correct answer.
I confirmed it for fun. Got 2.746 over 10000 trials. Close enough.
(average (map-n (fn ()
(1+ (position-if (let1 x 0
(fni (Re: How many draws of a random number [0,1] are needed to sum to 1
#8Isn't the pdf of a uniform distribution just f(x) = 1. What he gave was an exponential distribution with rate parameter lambda. The rest of the math seems correct. But the dependence on e is not surprising as it is relevant to the initial pdf. Am I missing something?
It's very easy to verify experimentally that e is likely the correct answer.
Doubly confirmed. 2.71832 over 100M trials.
import random
totalsteps = 0
for i in range(100000000):
sum = 0.0
steps = 0
while sum Re: How many draws of a random number [0,1] are needed to sum to 1
#9Isn't the pdf of a uniform distribution just f(x) = 1. What he gave was an exponential distribution with rate parameter lambda. The rest of the math seems correct. But the dependence on e is not surprising as it is relevant to the initial pdf. Am I missing something?
It's very easy to verify experimentally that e is likely the correct answer.
Yep: http://codepad.org/gIaWdVY9
EDIT: Beaten to it :)
Re: How many draws of a random number [0,1] are needed to sum to 1
#10Heh wrote about this (on my blog) a long, long ago. Was a fun numerical experiment to break the boringness of my own numerical experiments with fractals