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August 3rd, 2017, 05:05 PM  #1 
Senior Member Joined: May 2015 From: Arlington, VA Posts: 444 Thanks: 29 Math Focus: Number theory  Probability: discrete or continuous
Probability distributions can exist in two cases  discrete or continuous. Do they also exist as both?

August 3rd, 2017, 05:18 PM  #2 
Senior Member Joined: Oct 2009 Posts: 850 Thanks: 325  
August 4th, 2017, 12:19 AM  #3 
Senior Member Joined: May 2015 From: Arlington, VA Posts: 444 Thanks: 29 Math Focus: Number theory 
For every mixed probability distribution is there another one which serves as its complement, such as its Fourier transform? Do continuous distributions serve as complements to discrete distributions and vice versa? Is a parameter of a continuous probability distribution a discrete wavelength, and a parameter of a discrete probability distribution a continuous wavelength? 
August 4th, 2017, 03:02 AM  #4  
Senior Member Joined: Apr 2014 From: Glasgow Posts: 2,157 Thanks: 731 Math Focus: Physics, mathematical modelling, numerical and computational solutions 
Here's an answer from a physics perspective... Quote:
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Just in case you're not aware... some gases can be described by a density as a function of position $\displaystyle \rho(x,y,z)$ and such distributions can be assigned a meanfree path (as a constant or variable) which uses the symbol $\displaystyle \lambda$. This shouldn't be confused with wavelength. The meanfree path is the typical distance that something travelling within the medium can travel before colliding with something. Low density gases have a higher meanfree path and vice versa, so the meanfree path is dependent on the distribution of particles in the gas. Therefore, although wavelength is unlikely to be a relevant parameter for probability distributions, there are parameters that characterise actual distributions which are additional to the usual mean, variance, standard deviation and expectation variable. Therefore, although I can't think of any phenomena which use wavelength as a characteristic parameter of a distribution, it wouldn't shock me if you could find an application somewhere that does.  

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