A fault-tolerant system that processes transactions for a financial services firm uses three separate computers. If the operating computer fails, one of the two spares can be im- mediately switched online. After the second computer fails. the last computer can be immediately switched online. Assume that the probability of a failure during any transac- tion is 10" and that the transactions can be considered to be independent events.

(a) What is the mean number of transactions before all com- puters have failed?

(b) What is the variance of the number of transactions before all computers have failed?