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Math Help - product lifetime

  1. #1
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    Talking product lifetime

    Product lifetime is Y=5X^0.7 and X has exponential distribution of \lambda=1. Find distribution function and p.d.f. of Y.

    My Guess Work:

    So far, I know x=(y/5)^{10/7} and f(x)=e^{-x} since the mean is 1.

    When I take the derivative of the equation after substituting (y/5)^{10/7} for x, I get (-2/35)5^{4/7}y^{3/7}e^{(-1/25)5^{4/7}y^{10/7}}.

    Then multiplying the absolute value of this equation by the original equation of e^{(y/5)^{(10/7)}}, I get (2/25)e^{(-1/25)(5^{4/7}y^{10/7}}5^{4/5}e^{(-1/25)5^{4/7}R(y^{10/7})}|y|^{3/7}

    I really have no idea how to get the right answer to this problem.
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  2. #2
    MHF Contributor matheagle's Avatar
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    this question was asked two days ago
    1 y>0, so the absolute value is silly
    2 what is R?
    3 when you differentiate (y/5)^{10/7} it's better to rewrite this as {y^{10/7}\over 5^{10/7}}
    so you don't need to use the chain rule here.
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  3. #3
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    mr fantastic's Avatar
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    Quote Originally Posted by jennifer1004 View Post
    Product lifetime is Y=5X^0.7 and X has exponential distribution of \lambda=1. Find distribution function and p.d.f. of Y.

    My Guess Work:

    So far, I know x=(y/5)^{10/7} and f(x)=e^{-x} since the mean is 1.

    When I take the derivative of the equation after substituting (y/5)^{10/7} for x, I get (-2/35)5^{4/7}y^{3/7}e^{(-1/25)5^{4/7}y^{10/7}}.

    Then multiplying the absolute value of this equation by the original equation of e^{(y/5)^{(10/7)}}, I get (2/25)e^{(-1/25)(5^{4/7}y^{10/7}}5^{4/5}e^{(-1/25)5^{4/7}R(y^{10/7})}|y|^{3/7}

    I really have no idea how to get the right answer to this problem.
    Popular question. Asked and answered (in different ways) in the following threads:

    http://www.mathhelpforum.com/math-he...tial-dist.html

    http://www.mathhelpforum.com/math-he...ion-p-d-f.html

    http://www.mathhelpforum.com/math-he...ction-f-x.html

    Thread closed.
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