Markov's and Chebyshev's Inequalities

Let $X$ be a random variable on a probability space $(\Omega,\mathcal{F},P)$ and let $a>0$.

Markov's inequality. If $X\ge 0$ pointwise, then

with the expectation in $[0,\infty]$ (the inequality being trivial when the right side is infinite).

Chebyshev's inequality. If $X$ and $X^{2}$ have finite expectation, then

with the variance as defined there.