In exponential distribution, if I have a question saying what is the probability of waiting at least $18$ minutes given that I have waited $10$ minutes with mean $3$; How would I show that using $P(A|B)$?
2026-03-26 12:38:30.1774528710
Probability of waiting at least $18$ minutes given that I have waited $10$ minutes with mean $3$; How would I show that using $P(A|B)$?
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The thing about an exponential distribution is that it is memoryless i.e. the past has no implications on the future.
Hence the probability of waiting for 18 minutes given that you've waited for 10,
$$P(18|10)=P(8|0)=P(8)=e^{-\frac{8}{3}}$$
Here I've used the fact that the exponential distribution $p(x)=\lambda e^{-\lambda x }$ has mean $\frac{1}{\lambda}$ ($\therefore \lambda=\frac{1}{3}$ here)