Post on 05-Jan-2016
Discrete to Continuous
In each step each bar in the histogram is split into two bars.
• Now one final step, to an uncountably large number of bars, each infinitely narrow, yielding a continuous, uniform distribution ranging from A to B.
• Now I do the same but I start with a binomial distribution with p = .5 and three bars.
• Note that the bars are not all of equal height.
• Each time I split one, I lower the height of the tail-wards one more than the center-wards one.
• Now one final leap to a continuous (normal) distribution with an uncountably large number of infinitely narrow bars.