A system has two components: A and B. The operating times until failure of the two components are independent and exponentially distributed

A system has two components: A and B. The operating times until failure of the two components are independent and exponentially distributed random variables with parameter 2 for component A, and parameter 3 for component B. The system fails at the first component failure.
(a) – Read section 1.5.2 in the textbook.
(b) – What is the mean time to failure for component A and for component B

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  1. Answer:

    [tex]E(x) = \frac{1}{2}[/tex] — Component A

    [tex]E(x) = \frac{1}{3}[/tex] — Component B

    Step-by-step explanation:

    Given

    Distribution = Exponential

    [tex]\lambda = 2[/tex] — Component A

    [tex]\lambda = 3[/tex] — Component B

    Solving (a): The mean time of A

    The mean of an exponential distribution is:

    [tex]E(x) = \frac{1}{\lambda}[/tex]

    We have:

    [tex]\lambda = 2[/tex] — Component A

    [tex]E(x) = \frac{1}{2}[/tex]

    Solving (b): The mean time of B

    The mean of an exponential distribution is:

    [tex]E(x) = \frac{1}{\lambda}[/tex]

    We have:

    [tex]\lambda = 3[/tex] — Component B

    [tex]E(x) = \frac{1}{3}[/tex]

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