A system consists of five identical components connected in series asshown: ----1-----2-----3-----4-----5---- As soon as one component fails, the entire system will fail. Suppose eachcomponent has a lifetime that is exponentially distributed with λ= .01and that components fail independently of one another. Define events Ai [ith component lasts at least thours], i=1,..., 5, so that the As areindependent events. Let X= the time at which the system fails-that is,the shortest (minimum) lifetime among the five componentsa. The event {X≥t) is equivalent to what event involving A1,..., A5? b. Using the independence of the Ai's, compute P(X≥t). Then obtain F(t)= P(X≥ t) and the pdf of X. What type of distribution does Xhave?c. Suppose there are n components, each having exponentiallifetimewith parameter 1. What type of distributiondoes Xhave?
A system consists of five identical components connected in series as
shown:
----1-----2-----3-----4-----5----
As soon as one component fails, the entire system will fail. Suppose each
component has a lifetime that is exponentially distributed with λ= .01
and that components fail independently of one another. Define events Ai
[ith component lasts at least thours], i=1,..., 5, so that the As are
independent events. Let X= the time at which the system fails-that is,
the shortest (minimum) lifetime among the five components
a. The
b. Using the independence of the Ai's, compute P(X≥t). Then obtain F(t)
= P(X≥ t) and the
c. Suppose there are n components, each having exponentiallifetime
with parameter 1. What type of distributiondoes Xhave?
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