Statistics · Statistical distributions
Chapter 1 · 3
The idea
The continuous uniform distribution
When every value in an interval is equally likely: the rectangular probability density function, probability as length over width, the cumulative distribution function and quantiles, the mean, the variance and the exact value of E(X²), finding a and b from given facts, intervals that run past an end, and random cuts that split a length into pieces.
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Statistics · Statistical distributions
The continuous uniform distribution
When every value in an interval is equally likely: the rectangular probability density function, probability as length over width, the cumulative distribution function and quantiles, the mean, the variance and the exact value of E(X²), finding a and b from given facts, intervals that run past an end, and random cuts that split a length into pieces.
Why it works
Where will the rope snap?
A testing rig grips a m rope in two clamps, m and m from end , and pulls until the rope snaps. The rope is the same all along, so no point between the clamps is more likely to break than any other. Let m be the distance of the snap from .How likely is a snap more than m from ? The stretch from to is of the m between the clamps, so intuition says . This lesson turns that intuition into a model you can calculate with: the continuous uniform distribution.Keep reading — free
The rest of the explanation, plus 5 worked examples you step through move by move.
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