# Birds on a Wire

Birds on a Wire

A number of birds randomly land on a telephone wire. If the intervals between each bird and its closest companion were painted, what would be the expected fraction of wire painted? And what proportion of the number of intervals would be painted? The key to answering these questions is to realize that the probability distribution of interval lengths is (approximately) exponential. Knowing that, these fractions can be calculated to be 7/18 and 2/3.