Solution
= Solution
For a nonnegative <random variable> $Z$ and $a>0$, the pointwise inequality $Z\ge a\mathbf1_{\{Z\ge a\}}$ gives
$$
\boxed{\mathbb P(Z\ge a)\le\frac{\mathbb EZ}{a}.}
$$
= Solution
For a nonnegative <random variable> $Z$ and $a>0$, the pointwise inequality $Z\ge a\mathbf1_{\{Z\ge a\}}$ gives
$$
\boxed{\mathbb P(Z\ge a)\le\frac{\mathbb EZ}{a}.}
$$