How to calculate 95th percentile from mean and standard deviation of an exponential distribution?

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The q th q th quantile of a random variable XX is the value xx such that

Pr[X≤x]=q. Pr[X≤x]=q. So in your case q=0.25 q=0.25, and 0.25=Pr[X≤x] = FX (x) = 1 - e - x/β. 0.25=Pr[X≤x] = FX (x) = 1 - e - x/β. This gives us e - x/4 = 0.75 e - x/4 = 0.75, or x=-4log0.75≈1.15073. x=-4log⁡0.75≈1.15073. This assumes that the parametrization of the exponential distribution is by scale; i. e., if β=4 β=4 this means E[X]=β=4 E⁡[X]=β=4, rather than by rate--in which case E[X]=1/β=1/4 E⁡[X]=1/β=1/4.