Basic q I'm sure. Markov's inequality states that the upper bound to the probability that the realization of a random variable exceeds a given threshold is defined thus:
$P(|X| \ge c) \le \frac{E[X]}{c}$
so if E[X] is 100 and c is 150 I get a probability of $\frac{100}{150}$ = 0.66
No problem so far. However, if E[X] = 100 and c = 50, I get a probability of $\frac{100}{50}$ = 2
which is obviously wrong. Most examples online have a c value greater the the expected value. Can someone clarify please?
Best Answer
Markov inequality does not give a probability but a bound. And $P(\text{something})\le 2 $ is not wrong, but, on the contrary always true. Because it's a trivial truth (we already had a better bound: $1$) the bound is in this case (still valid but) useless.