# Probability distributions

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?

• Using uniform distribution, my answer will be 0.1. Seems very sloppy though. – siangkang May 21 '13 at 7:09
• Exponential: Radioactive decay – siangkang May 21 '13 at 7:14
• 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. – anna v May 21 '13 at 7:27
• alright thanks! @Qmechanic: dunno that stats.stackexchange existed till now, I posted it here because I was reading a physics textbook, thanks anyway. – siangkang May 21 '13 at 8:36
• @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. – wolfies May 21 '13 at 8:44

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.
• +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. – whuber May 21 '13 at 14:30