Cauchy-Distributed Random Numbers A Cauchy-distributed random variable has the density function fc(x) := c 1 c2 + x2 . Show that its distribution function

Cauchy-Distributed Random Numbers A Cauchy-distributed random variable has the density function fc(x) := c π 1 c2 + x2 . Show that its distribution function Fc and its inverse F −1 c are Fc(x) = 1 π arctan x c + 1 2 , F −1 c (y) = c tan(π(y − 1 2 )). How can this be used to generate Cauchy-distributed random numbers out of uniform deviates?