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  • Exam P question

    This problem is similar to an Soa Question, but this time it asks for expected value of the min(X,Y), and I am not sure of how to go about doing the problem

    The problem is:

    An electronic device consists of two components. The lifetimes of the two components are identically distributed with the following common density function:

    f_x(x)={3/2e^-3x +9/2e^-9x} for x >0

    The device will break down if any of the two components fails. Find the epected lifetime of the device.

    ans: a. 18 b. 12 c. 9 d. 6 e. 3

    Thank you

  • #2
    The formula for the order statistic (minimum out of n) density is

    f1(x)=n((1-F(x))^(n-1))f(x)

    Note f refers to density whereas F refers to distribution.

    In this case n=2 as you want the density and expected value of the first failure (assuming they are independent).

    It's best to not just memorize the order stat densities but to understand them. They are very intuitive. Once you understand them you won't have to memorize them.

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