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# Properties of The Quantile Function $t(p)$

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- Relates the time at which $100p\%$ of a population will have failed <focus>the inverse of the cdf</focus> 

$$t_{p}=F^{-1}(p)$$

- In general, $t_{p}$ is defined as the <red>smallest</red> time $t$ satisfying $F(t)=p$, 

$$t_{p}=\min(t)|P(T\le t)=F(t)\ge p$$ 
