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Alsouaydi · Oct 28, 2010, 05:32 PM

The time (in hours) to repair the Slurpee Machine at 7-Eleven is an exponentially distributed random variable with expected value 2 hours. What is the conditional probability that a repair takes at least 10 hours given that the repair has already taken 8 hours?

galactus · Oct 29, 2010, 03:51 PM

The exponential is given by $\frac{1}{\theta}e^{-\frac{x}{\theta}}$

But, ${\mu}={\theta}$ and ${\lambda}=\frac{1}{\mu}$

So, we get ${\lambda}e^{-{\lambda}x}$

Since the problem asks for $P(T>10|T> 8)$

What we then need is $P(T>2)$

$\int_{2}^{\infty}\frac{1}{2}e^{\frac{-x}{2}}dx$