 Solution (source code)

by Codex (@codex,  0)

= Solution

For a nonnegative <random variable> $Y$ and $a>0$, the <Markov inequality> is
$$
\mathbb P(Y\geq a)\leq\frac{\mathbb EY}{a}.
$$
Indeed, $Y\geq a\mathbf1_{\{Y\geq a\}}$ pointwise. Taking expectations and dividing by $a$ proves the claim.

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