Uniform Distributions

             After class yesterday I was thinking about the distributions that we viewed regarding days of birth in a month or coin flips and was wondering what the best way to graphically represent them.  After doing a bit of research I remembered that in my introductory statistics class we talked about these types of distributions as being Uniform Distributions.  Because these numbers are discrete, there is a finite number of probable outcomes which are all equally likely and the Gaussian Distribution is inappropriate for their representation.  To harken back to the course discussion of coin flips, Javier and Mika notwithstanding, if you have an evenly weighted coin the number of flips should be exactly equal for both sides given an appropriate number of flips.  The same can be said for a die toss where the die is equally weighted.
 
             Interestingly I wondered what the real world application of this formula would be in a practical sense.  Wikipedia describes the German Tank Problem where allied forces attempted to estimate German tank production during the World War II.  Gaussian distribution is not appropriate for this particular estimation because we know that the probability of zero is zero because of visual confirmation of at least one tank; however, the number is finite and uniform in its presentation.  There is a link provided on the page linked below if you would like some additional information about the calculations, which aren't as ugly as you'd think, and it allows for the examination of other practical uses for the uniform distribution.

Sources: Retrieved on 2/6/2013
 http://en.wikipedia.org/wiki/Uniform_distribution_%28discrete%29