Fraction of a Circle Covered by Arcs of a Given Length

number of arcs

n

2

arc length

a

1

10

μ = 0.1900 σ = 0.0238

This Demonstration shows the probability density function for the fraction of a circle with unit circumference covered by

n

random arcs, each of length

a

. This probability distribution is a mixed distribution. The discrete probability mass

p

is shown and captioned in red, and the continuous probability density is shown in blue (scaled by

a

).

μ

and

2

σ

are the mean and variance of the fraction covered.