ABSTRACT
The Markov inequality∗ states that the probability that the absolute value of a random variable is greater than or equal to a > 0 is less than or equal to E(|X|)/a. Its proof is straightforward and proceeds as follows:
P (|X| ≥ a) = ∫ |α|≥a
fX(α) dα
≤ ∫ |α|≥a
|α| a fX(α) dα
= 1 a
∫ |α|≥a
|α|fX(α) dα
≤ 1 a
|α|fX(α) dα
=
a .
