I got an question:

A dice determine the scores based on density with k = 2.

f(x) = ( k 1/x^{k+1} , for x 1,

0, otherwise,

the random variable Z : [1, ) [0, 1], x 1/x and the mapping

S(x) =

0, if 0 x < 1/4 ,

1, if 1/4 x < 2/4 ,

2, if 2/4 x < 3/4 ,

3, if 3/4 x 1.

how to show that the CDF of f is F(x) = 1 (1/x^2) for x 1

an how to derive its inverse F^{1}(y) for y [0, 1)