Question
The time $T$ required to repair a machine is an exponentially distributed random variable with mean $\frac{1}{2}$ (hours).(a) What is the probability that a repair time exceeds $\frac{1}{2}$ hour?(b) What is the probability that a repair takes at least $12 \frac{1}{2}$ hours given that its duration exceeds 12 hours?
Step 1
The mean of the exponential distribution is given as \(\frac{1}{2}\) hours. The rate parameter \(\lambda\) is the reciprocal of the mean, so we have: \[ \lambda = \frac{1}{\text{mean}} = \frac{1}{\frac{1}{2}} = 2 \text{ hours}^{-1}. \] Show more…
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