The Cauchy distribution has the density function which is symmetric about zero....

The Cauchy distribution has the density function

which is symmetric about zero. This distribution has very heavy tails, which cause the arithmetic mean to be a very poor estimate of location. Simulate the distribution of the arithmetic mean and of the median from a sample of size 25 from the Cauchy distribution by drawing 100 samples of size 25 and compare. From Example B in Section 3.6.1, if Z₁ and Z₂ are independent and N(0, 1), then their quotient follows a Cauchy distribution. (This gives a simple way of generating Cauchy random variables.)