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What is the probability that a random number [0,1) will lie in [0.5,0.6]?

As far as I know, there are 3 probability distributions in physics we usually use, but I am not sure when we can use Gaussian, Exponential and uniform distribution. Any examples?

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  • $\begingroup$ Using uniform distribution, my answer will be 0.1. Seems very sloppy though. $\endgroup$
    – siangkang
    Commented May 21, 2013 at 7:09
  • $\begingroup$ Exponential: Radioactive decay $\endgroup$
    – siangkang
    Commented May 21, 2013 at 7:14
  • $\begingroup$ When you prescribe "random number" by definition it is the uniform distribution. The one that tells us that throwing a dice will come up with the face six 1/6th of the time. $\endgroup$
    – anna v
    Commented May 21, 2013 at 7:27
  • $\begingroup$ alright thanks! @Qmechanic: dunno that stats.stackexchange existed till now, I posted it here because I was reading a physics textbook, thanks anyway. $\endgroup$
    – siangkang
    Commented May 21, 2013 at 8:36
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    $\begingroup$ @anna wrote: When you prescribe "random number" by definition it is the uniform distribution ... not at all. There are infinitely many distributions with domain of support on (0,1). A random variable whose distribution has not been specified is just a random variable whose distribution has either not been specified, or is not known. $\endgroup$
    – wolfies
    Commented May 21, 2013 at 8:44

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Firstly, it depends what kind of random number it is. If you flip two coins(0/1) and take the average (technically in [0,1]), you'll get a very different kind of random number than if you say every number [0,1) is equally likely to be chosen.

Secondly, looking at the three you mention, if you're interested in [0,1) exponential or gaussian would be bad models as they take values in $[0, \infty)$ and $(-\infty, \infty)$ respectively. Uniform(0,1) would be the natural choice, but as above, other brands are available.

The mass of the function in [0.5, 0.6] will entirely depend what distribution is used. If Uniform(0,1) then 0.1.

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  • $\begingroup$ +1. Moreover, there are no effective bounds on the probability, either. When the number is Uniform$[.5,.6]$ the probability is $1$ and when the number if Uniform$[0,.1]$ the probability is $0$; all probabilities are possible under some circumstances. $\endgroup$
    – whuber ♦
    Commented May 21, 2013 at 14:30

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