Q27Single correct4 Marks3 Sep 2023

The time it takes for a computer system to reboot after a crash follows an exponential distribution with a mean of 2 hours. What is the probability that the system will be back online within 1 hour of the crash?

A

1 - e^-2

B

1 - e^-0.5

C

e^-2

D

$e^-0.5 The cumulative distribution function (CDF) of an exponential distribution is given by F(t) = 1 - e^{-\lambda t} for t \ge 0. We need the probability that reboot completes within 1 hour: P(T \le 1) = F(1) = 1 - e^{-0.5 \cdot 1} = 1 - e^-0.5.$