(a) Plot on the same set of axes, using different line types and/or different colors, the PDFs of a standard normal distribution, a \(t\) with 10 degrees of freedom, a \(t\) with 2 degrees of freedom, and a Cauchy.

Briefly discuss the plots.

(b) Show that the mean and variance of the Cauchy distribution do not exist (or are infinite, depending on your definition of the improper integrals).