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$$\Pr\{X>(1+\delta)\mu\}<-e^{-\delta^2\mu/3}$$

How do I say the first part of the Probability equation in English - just the portion before '=' sign? Thanks.

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    $\begingroup$ There is no equal sign in your equation. $\endgroup$ – SchrodingersCat Oct 12 '16 at 5:40
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    $\begingroup$ It looks like rubbish, probabilities lie in $[0,1]$ and cannot be negative. $\endgroup$ – copper.hat Oct 12 '16 at 5:41
  • $\begingroup$ @copper.hat I got that from some lecture notes - cs.cmu.edu/~haeupler/15859F15/docs/lecture04.pdf $\endgroup$ – glendon Oct 12 '16 at 7:08
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    $\begingroup$ It must be a typo., I presume it should be $1-\cdots$. $\endgroup$ – copper.hat Oct 12 '16 at 13:25
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The probability that a random variable $X$ deviates from its mean $\mu$ by more than a fraction $\delta$ is less that $-e^{-\frac{\delta^2\mu}{3}}$

Note that $\mu$ is not necessarily the mean of $X$. I am calling it the mean because these kinds of bounds are called tail bounds and typically are used to bound the deviation of a random variable from its mean.

Also on a different note, the RHS is negative which doesn't make sense in case of probabilities.

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The equation should be read as :

The probability that the random variable $X$ assumes a value greater than $(1+\delta)\mu$ is less than $-e^{-\frac{\delta^2\mu}{3}}$, $\mu$ being the mean of $X$.

Although the equation makes no sense as copperhat has already commented: probabilities are always within the interval $[0,1]$.

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