How do I rewrite a conditional distribution that is an inequality as a function of another variable?
The problem I have been posed is the following:
Given
$F_u(y) = \mathbb{P}[A-u \le y | A > u]$
Show that this can be rewritten as
$F(x) = 1 - (1-F(u))(1-F_u(x-u))$