Question

A stick of length 1 is broken at a uniformly random point, yielding two pieces. Let x and y be the lengths of the shorter and longer pieces, respectively, and let r represent the ratio x/y. What is the distribution of r?

a) Normal distribution
b) Uniform distribution
c) Exponential distribution
d) Binomial distribution

Answer 1

The distribution of the ratio r of the lengths of the shorter and longer pieces when a stick of length 1 is uniformly randomly broken is a) Uniform distribution.

Step-by-step explanation:

The distribution of the ratio r of the lengths of the shorter and longer pieces when a stick of length 1 is uniformly randomly broken is:

b) Uniform distribution

Step-by-step explanation:

Since the stick is broken at a uniformly random point, any point along the length of the stick is equally likely to be chosen. This means that the shorter piece can have any length from 0 to 1, and the longer piece can have any length from 0 to 1. Therefore, the ratio r can take on any value between 0 and 1.

The uniform distribution is characterized by constant probability throughout its support (0 to 1 in this case). Therefore, the distribution of r is a uniform distribution.