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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.

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discrete to continuous

Discrete to Continuous

In each step each bar in the histogram is split into two bars.

slide6
Now one final step, to an uncountably large number of bars, each infinitely narrow, yielding a continuous, uniform distribution ranging from A to B.
slide8
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.
slide15
Now one final leap to a continuous (normal) distribution with an uncountably large number of infinitely narrow bars.
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