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Why Things Don’t Add Up

Last time we learned about continuous distributions and how they are described by the frequency function. I also promised to save us from the infinitesimal probabilities represented in the frequency function. The answer is the Cumulative Distribution Function (CDF) , which is merely the area under the frequency function curve to the left of a given point. (You may remember with horror from your schooldays that the way to get this area is to integrate the curve, but we need not worry about the mechanics of this here.) What matters is that the area to the left of any value x represents not the probability of the variable being exactly x (which is infinitesimal) but the probability that it is less than x. And this is a nice finite number, varying of course from 0 to 1 as x increases from some suitably low value (minus infinity if you like) and a high one (plus infinity). Furthermore, this cumulative probability is what we are generally interested in. (We rarely care whether the project will finish on a particular date, but rather whether it will finish by a particular date.) So now we are cooking with gas! The cumulative curve is generally in the shape of an S (since its gradient is at its highest at a point coinciding with the peak of the frequency function) and is sometimes called an S-curve.

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Why Things Don’t Add Up

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