77. A system consists of five identical components connected in series as shown: 2 3 As soon as one component fails, the entire system will fail. Suppose each component has a lifetime that is exponentially distributed with 2 = .01 and that components fail independently of one another. Define events A; = {ith component lasts at least 1 hours}, i = 1, . , 5, so that the A,'s 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, . .. , Ag? b. Using the independence of the five A¡'s, com- pute P(X > 1). Then obtain F(t) = P(X < 1) and the pdf of X. What type of distribution does X have? c. Suppose there are n components, each having exponential lifetime with parameter â. What type of distribution does X have?
77. A system consists of five identical components connected in series as shown: 2 3 As soon as one component fails, the entire system will fail. Suppose each component has a lifetime that is exponentially distributed with 2 = .01 and that components fail independently of one another. Define events A; = {ith component lasts at least 1 hours}, i = 1, . , 5, so that the A,'s 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, . .. , Ag? b. Using the independence of the five A¡'s, com- pute P(X > 1). Then obtain F(t) = P(X < 1) and the pdf of X. What type of distribution does X have? c. Suppose there are n components, each having exponential lifetime with parameter â. What type of distribution does X have?
MATLAB: An Introduction with Applications
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Author:Amos Gilat
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Chapter1: Starting With Matlab
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Related questions
Question
![77. A system consists of five identical components
connected in series as shown:
1
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 2 = .01 and
that components fail independently of one
another. Define events A; :
at least t hours }, i = 1, ... , 5, so that the A;'s 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, ..., As?
b. Using the independence of the five A;'s, com-
pute P(X > t). Then obtain F(t) = P(X < 1)
and the pdf of X. What type of distribution
{ith component lasts
does X have?
c. Suppose there are n components, each having
exponential lifetime with parameter å. What
type of distribution does X have?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd6646334-68c1-47ca-ae71-cb8110fb90b4%2Fe6b4e03b-b6bd-42ae-bc0d-ebaebae5b483%2Fwpc6fza_processed.png&w=3840&q=75)
Transcribed Image Text:77. A system consists of five identical components
connected in series as shown:
1
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 2 = .01 and
that components fail independently of one
another. Define events A; :
at least t hours }, i = 1, ... , 5, so that the A;'s 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, ..., As?
b. Using the independence of the five A;'s, com-
pute P(X > t). Then obtain F(t) = P(X < 1)
and the pdf of X. What type of distribution
{ith component lasts
does X have?
c. Suppose there are n components, each having
exponential lifetime with parameter å. What
type of distribution does X have?
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