Question

(1 point) Suppose that the time (in hours) required to repair a machine is an exponentially distributed random variable with parameterA- 0.6. What is (a) the probability that a repair time exceeds 10 hours? (b) the conditional probability that a repair takes at least 11 hours, given that it takes more than 8 hours?

Answer 1

$P(X>x)=e^{-\lambda*x}$

a) P(X > 10) = e^{-0.6 * 10} = 0.002479

b) P(X > 11 | X > 8) = P(X > 11) / P(X > 8) = e^-0.6*11 / e^-0.6*8 = e^-0.6*3 = 0.1653