Uniform distribution
A uniform distribution on the range a to b makes every stretch of equal width equally likely. Its mean is (a + b) / 2 and its variance is (b - a) squared / 12.
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Analogy
A spinner with no favourite colour. Every angle is as likely as any other.
Example
Wait uniform from 0 to 20 minMean = (0 + 20) / 2 = 10Variance = 400 / 12 = 33.3P(wait < 5) = 5 / 20 = 0.25
In practice
Models a random waiting time when you do not know the timetable, or a random number generator.
Practice
Flashcards
- Mean of a uniform distribution from a to b?(a + b) / 2.
Questions people ask
How do I find probabilities for a uniform distribution?
Find the width of the interval you want and divide by the total width b minus a. For a wait uniform between 0 and 20 minutes, the chance of waiting between 5 and 10 minutes is 5 divided by 20, which is 0.25.
Is the mean of a uniform distribution always the midpoint?
Yes. The density is flat, so the balance point sits exactly halfway between a and b. The median is the same point. Unlike the normal curve, the uniform has hard edges: no value outside a to b can happen, so the model suits a bounded range only.