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Math Help - distribution function and p.d.f.

  1. #1
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    distribution function and p.d.f.

    The lifetime (in years) of a product is Y=5X^{0.7} where X has an exponential distribution with mean one. Find the distribution function and p.d.f. of Y.

    Thank you in advance.
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  2. #2
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    Quote Originally Posted by calabrone View Post
    The lifetime (in years) of a product is Y=5X^{0.7} where X has an exponential distribution with mean one. Find the distribution function and p.d.f. of Y.

    Thank you in advance.
    I'd calculate the cdf of Y and then differentiate to get the pdf:

    F(y) = \Pr(Y < y) = \Pr(5 X^{0.7} < y) = \Pr \left( X^{0.7} < \frac{y}{5} \right) = \Pr \left( X < \left( \frac{y}{5} \right)^{10/7} \right)  = \int_0^{\left( \frac{y}{5} \right)^{10/7}} g(x) \, dx

    where g(x) is the pdf of X.
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  3. #3
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    Quote Originally Posted by calabrone View Post
    The lifetime (in years) of a product is Y=5X^{0.7} where X has an exponential distribution with mean one. Find the distribution function and p.d.f. of Y.

    Thank you in advance.
    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...ction-f-x.html

    http://www.mathhelpforum.com/math-he...-lifetime.html

    Thread closed.
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