Problem 5E

The lifetime of a laser (in hours) is lognormally distributed with µ = 8 and σ2 = 2.4. Two such lasers are operating independently.

a. Use a simulated sample of size 1000 to estimate the probability that the sum of the two lifetimes is greater than 20,000 hours.

b. Estimate the probability that both lasers last more than 3000 hours.

c. Estimate the probability that both lasers fail before 10,000 hours.

Solution:

Step 1 of 3:

The lifetime of a laser (in hours) is lognormally distributed with mean 8 and . Two lasers are operating independently.

We have to estimate

- The probability that the sum of two lifetimes is greater 20,000 hours by using a simulated sample of size 1000..
- The probability that both lasers last more than 3000 hours.
- The probability that both lasers fail before 10,000 hours.