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Math Help - Probability of shelf life (in hours)

  1. #1
    Yan
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    Probability of shelf life (in hours)

    The shelf life (in hours) of a certain perishable packaged food is a random variable whose probability density function is given by

    f(x)=20,000/((x+100)^3) for x>0 and =0 elsewhere

    Find the probabilities that one of these packages will have a shelf lift of
    (a) at least 200 hours
    (b) at most 100 hours
    (c) anywhere from 80 to120 hours
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by Yan View Post
    The shelf life (in hours) of a certain perishable packaged food is a random variable whose probability density function is given by

    f(x)=20,000/((x+100)^3) for x>0 and =0 elsewhere

    Find the probabilities that one of these packages will have a shelf lift of
    (a) at least 200 hours
    this is asking for P \{ X \ge 200 \} = \int_{200}^\infty f(x)~dx

    (b) at most 100 hours
    this is asking for P \{ X \le 100 \} = \int_{- \infty}^{100} f(x)~dx = \int_0^{100} f(x)~dx

    (c) anywhere from 80 to120 hours
    this is asking for P \{ 80 \le X \le 120 \} = \int_{80}^{120} f(x)~dx


    i leave it to you to evaluate the integrals. hopefully you can
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