Chapter 7

Chapter 7 Page 313

exercise 11.

11 A company buys 100 lightbulbs, each of which has an exponential lifetime of 1000 hours. What is the expected time for the first of these bulbs to burn out?

Answer: Let \(X_{1}, X_{2},...,X_{100}\) be 100 lightbulbs with exponential lifetime \(\mu=1000\). The first lightbulb will fail at minimum value of \(X_{j}\) suppose that is M. The denisity of M is exponential with mean \(\mu/100\)

mu <- 1000
n <- 100
mu/n
## [1] 10

The expected time for the first bulb to fail out is 10 hours.