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Math Help - Hopefully a quite simple integration problem

  1. #1
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    Hopefully a quite simple integration problem

    Hi! I've got this problem:

    The weekly repair cost Y for a machine has pdf given by:

    f(y) = 3(1-y)^{2}, 0<y<1
    and 0 elsewhere

    w. measurements in hundreds of dollars. How much money should be budgeted each week for repair cost so that the actual cost will exceed the budgeted amount only 10% of the time?

    The problem is that I don't know where to start. Should I calculate
    P (budgeted cost < actual cost) = .10? I don't understand how I should think and what I need to calculate. I've calculated E(Y) and that's = 1/4, but I don't know what I should use it for. Can anyone guide me in the right direction?

    Thankful for any help and suggestions.
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  2. #2
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    Quote Originally Posted by approx View Post
    Hi! I've got this problem:

    The weekly repair cost Y for a machine has pdf given by:

    f(y) = 3(1-y)^{2}, 0<y<1
    and 0 elsewhere

    w. measurements in hundreds of dollars. How much money should be budgeted each week for repair cost so that the actual cost will exceed the budgeted amount only 10% of the time?

    The problem is that I don't know where to start. Should I calculate
    P (budgeted cost < actual cost) = .10? I don't understand how I should think and what I need to calculate. I've calculated E(Y) and that's = 1/4, but I don't know what I should use it for. Can anyone guide me in the right direction?

    Thankful for any help and suggestions.
    You require the value of a such that \Pr(Y > a) = 0.1. Therefore solve for a in the following:

    \int_{a}^{1} 3 (1 - y^2) \, dy = 0.1.
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