We investigate the effect on the Cauchy distribution under a change of units. a. Let X have a standard Cauchy distribution. What is the distribution of Y = rX + s? b. Let X have a Cau(α, β)...

We investigate the effect on the Cauchy distribution under a change of units.

a. Let X have a standard Cauchy distribution. What is the distribution of Y = rX + s?

b. Let X have a Cau(α, β) distribution. What is the distribution of the random variable (X − α)/β?