1. Feb 23, 2013

### BrownianMan

For watches produced by a certain manufacturer, lifetimes follow a single-parameter Pareto distribution with alpha > 1 and theta = 4. The expected lifetime of a watch is 8 years.

a) Calculate the probability that the lifetime of a watch is at least 6 years.
b) For the same distribution as above, calculate the expected life of a watch that has already survived 6 years.

I did part a) and got the right answer: 0.444.

For (b): the lifetime L = 6+R, where R = remaining life: ER is calculated using the conditional density $f_X(x| X \geq 6).$