poisson distribution

the required to repair a machine is an exponential random variable with rate x=0.5 downs per hour.what is the probability that a repair time exceeds 2 hours?
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Mean time of downs or failures = 1/0.5=2 hrs. f(t)=0.5e^-0.5t is the exponential distribution probability equation where t=time in hours. Therefore f(2)=0.5e^-1=0.1839 or 18.39%. This is the probability of a failure occurring in 2 hours, causing the repair to exceed 2 hours.

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