As soon as one components fails, the entire system will fail. Suppose each component has a lifetime that is exponentially distributed with ? = 0.01 and that components fail independently of one...

As soon as one components fails, the entire system will fail. Suppose each component has a lifetime that is exponentially distributed with ? = 0.01 and that components fail independently of one another. Define eventsA_i
 = {ith component lasts at leastt hours},i = 1, . . . , 5, so that theA_i
s are independent events. LetX = the time at which the system fails—that is, the shortest (minimum) lifetime among the five components.

P(X ≥t)?

F(t) =P(X ≤t)?

the pdf ofX?