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Math Help - Distribution of time that a flashlight can operate

  1. #1
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    Question Distribution of time that a flashlight can operate

    I am wondering if I can get help on the following problem:
    If we have a stock of n batteries, each has a lifetime that is exponential
    with parameter c and they are independent of each other.
    If a flashlight needs 2 batteries, what is the lifetime that the flashlight can operate?
    I have 2 solutions that I can think of:
    1) The lifetime of the minimum (X,...Xn).
    2) The lifetime of the min(Xi,Xj) multiply by all possible pairs, 2 choose n.
    Any suggestion???
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  2. #2
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    Quote Originally Posted by thomas_donald View Post
    I am wondering if I can get help on the following problem:
    If we have a stock of n batteries, each has a lifetime that is exponential
    with parameter c and they are independent of each other.
    If a flashlight needs 2 batteries, what is the lifetime that the flashlight can operate?
    I have 2 solutions that I can think of:
    1) The lifetime of the minimum (X,...Xn).
    2) The lifetime of the min(Xi,Xj) multiply by all possible pairs, 2 choose n.
    Any suggestion???
    Do you mean "... what is the minimum possible lifetime that the flashlight can operate?" Then it will be minimum (X,...Xn).
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  3. #3
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    Sorry for the late response. Thank you very much for your help.
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