69. A system consists of five identical components connected in series as shown:

As soon as one component fails, the entire system will fail.

Suppose each component has a lifetime that is exponentially distributed with 
.01 and that components fail independently of one another. Define events Ai
{ith component lasts at least t hours}, i
1, . . . , 5, so that the Ais are independent events. Let X
the time at which the system fails—that is, the shortest (minimum) lifetime among the five components.

a. The event {X  t} is equivalent to what event involving A1, . . . , A5?

b. Using the independence of the Ais, compute P(X  t).

Then obtain F(t)
P(X  t) and the pdf of X. What type of distribution does X have?

c. Suppose there are n components, each having exponential lifetime with parameter . What type of distribution does X have?