I want to prove that $\displaystyle Pr( Z \ge a) \le {E(g(Z)) \over g(a)} $ given that $\displaystyle g(x) \ge 0 \forall x \in\mathbb{R} $ and that for any

$\displaystyle x_1, x_2 \mbox{ if }x_1 < x_2 \mbox{ then }g(x_1) < g(x_2) $.

Finally I was given the formula

$\displaystyle I_{[z \ge a]} = \left\{\begin{matrix} 1, & \mbox{if }z \ge a \\ 0, & \mbox{otherwise} \end{matrix}\right.$

and the inequality

$\displaystyle g(a)I_{[Z \ge a]} \le g(Z)I_{[Z \ge a]} \le g(Z) $

which I am supposed to use somehow.

Any help will be appreciated.