This applet plots 400 points as x varies from x = -10 to x = +10. The vertical axis shows the value of f(x) minus g(x), where f(x) is the normal density, and g(x) is the Cauchy density. The blue area corresponds to the region f(x)>g(x), while the red area corresponds to the region g(x)>f(x). The Cauchy distribution has much greater probability in the extreme tails.