I am taking Intro Prob and Stats and trying to better understand the concept of the Markov and Chebyshev inequalities method. After perusing proofs and examples, it's still unclear to me how to estimate the probabilities of an RV with bounds [0,n].
Say we are given a continuous RV with $E(X)=Var(X)=K$, and we want to find $P(X \in (0,1))$.
Using the Markov inequality we get:
$P(X\geq 0) \leq \frac{E(X)}{0}$, which makes it impossible to calculate.
Are there any tricks I am missing?
Best Answer
Trick is $\Pr(X>1)\le K$ so $\Pr(X\le 1)\ge 1-K$.
Note the Markov inequality only matters when the number being compared to is greater than the mean. So $1>K$ gives some results but otherwise vapid truths.
Only positive numbers are allowed, no $0$ or negatives.