A system using a component as describe in Homework 10 Question 8, with failure rate10% per day, is sent up in a satellite together with four spares components of the same type. As soon as the a component fails, it is replaced by a working spare. If Ti denotes the operating time of component i, then Ttotal = T1 + T2 + T3 + T4 + T5 denotes the total operating time. Compute:

(1) E[Ttotal];

(2) SD[Ttotal];

(3) P(Ttotal 90 days).

(4)How many spares must be provided so that P(Ttotal 90 days) is at least 90%?