How to describe this mathematical bound in English?

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

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

• There is no equal sign in your equation. – SchrodingersCat Oct 12 '16 at 5:40
• It looks like rubbish, probabilities lie in $[0,1]$ and cannot be negative. – copper.hat Oct 12 '16 at 5:41
• @copper.hat I got that from some lecture notes - cs.cmu.edu/~haeupler/15859F15/docs/lecture04.pdf – glendon Oct 12 '16 at 7:08
• It must be a typo., I presume it should be $1-\cdots$. – copper.hat Oct 12 '16 at 13:25

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.
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 $[0,1]$.