Visual Statistics Studio

 

 

Circle and the Normal Distribution

How come that one of the parameters of the ordinate of the normal distribution

 

                                                         

 

is π?

 

Also, the above formula can be written as the special case of the Euler's Gamma function

 

                                                          

 

where the constant a equals

 

                                                            

 

i.e., .3989, thus

                                                         

 

The area under the binomial has to be rescaled (horizontally and vertically) that, for infinite number of cases, will equal one. This integration is quite complex and, at one point, reads

 

                                                         

 

Lord Kelvin once said that “A mathematician is someone to whom it is obvious that .”  In visual statistics we can gain this kind of insight by plotting the binomial in 3-D

 

 

and rotating it as to view it from the bird’s eye view

 

 

with the polygon of the binomial distribution approximating the circle we would see if we plotted the normal distribution.