Expected Lifetime of Watches with Pareto Distribution

[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.

Not sure about part b). Wouldn't the answer be 8 years?

 

[Ray Vickson]

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.

Not sure about part b). Wouldn't the answer be 8 years?

Different articles on Pareto distributions use different names for the parameters, so it is not clear what you mean by α and θ. Please describe in more detail, or give a formula for the density function, or something similar.

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