A company buys 100 lightbulbs, each of which has an exponential lifetime of 1000 hours. What is the expected time for the rst of these bulbs to burn out? (See Exercise 10.)
** Solution ** Lets \((X_i - X_n)\) be independent variables with parameters $_i …_n $ \(Pr(k|X_k = minX_i...X_n) = \frac {\lambda_k}{\lambda_i ...\lambda_n}\) $i = , {_i} = $ \(\mu = 1000, n = 100\)
mu = 1000
bulb_n = 100
cat("The Expected time for the first of these bulbs to burn out is ", mu/bulb_n ,"hours ")## The Expected time for the first of these bulbs to burn out is 10 hours