$ξ$ and $η$ are independent random variables with distribution functions $F(x)$ and $G(x)$ correspondingly.
How do you find the distribution functions of random variables listed below in terms of a combination of $F(x)$ and $G(x)$?
$ζ_1=max(\xi,\eta)$
$ζ_2=min(\xi,\eta)$
$ζ_3=max(ξ,2η)$
Figured it out right after drhab hint.
$\zeta_1 = $ $P(\zeta_1≤x)$ = $P(\zeta≤x \land \eta ≤x)$ = $F(x)G(x)$
$\zeta_2 = $ $P(\zeta_2≤x)$ = $P(\zeta≤x \lor \eta ≤x)$ = $F(x) + G(x) - F(x)G(x)$.
$\zeta_3 = $ $P(\zeta_3≤x)$ = $P(\zeta≤x \land 2\eta ≤x)$ = $F(x)G(\frac{x}{2})$.