---
title: "Markov Inequality"
canonical: "https://modelassist.epixanalytics.com/space/EA/26574958/Markov%20Inequality"
format: markdown
---
The Markov Inequality gives some indication of the range of a distribution, in a similar way to [Tchebysheff's rule](https://epixanalytics.atlassian.net/wiki/spaces/EA/pages/26574957/). It states that for a *non-negative* random variable *X* with mean *m*:

![image](media://80839439-c216-4e3c-ad5f-74e1f482022b)


> Macro (mathblock)

 

for any constant *k* greater than *m*.

 

So, for example, for a random variable with mean 6, the probability of being greater than 20 is less than or equal to 6/20 = 30%.

 

Of course, being very general like Tchebysheff's rule, it makes a rather conservative statement. For most distributions, the probability is much smaller than *m/k*. For example:

 

|  |  |
| --- | --- |
| **Distribution with *****m*****=6** | **P(X ≥ 20)** |
| Exponential(6) | 3.6% |
| ChiSq(6) | 0.3% |
| Gamma(2,3) | 1% |
| Inverse Gaussian(6,*l*) | Max of 6.9% |
| Lognormal(6,*s*) | Max of 6.0% |
| Pareto(*q*,6(*q  *- 1)/*q*) | Max of 3.21% |

 

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