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Probability Weibull Distribution

  1. Apr 7, 2013 #1
    1. The problem statement, all variables and given/known data

    Suppose that x has a Weibull distribution with parameters [itex]\alpha[/itex] and [itex]\beta[/itex] and that [itex]P(x \leq 1)=.105[/itex] and [itex]P(2 \leq x)=.641[/itex]. What are [itex]\alpha[/itex] and [itex]\beta[/itex]?

    2. Relevant equations

    [itex]F(x) = 1 - e^{-(\frac{x}{\beta})^{\alpha}}[/itex]

    3. The attempt at a solution

    When I try and solve I get

    [itex]ln(.641) = -(\frac{1}{\beta})^{\alpha}[/itex]
    [itex]ln(.895) = -(\frac{1}{\beta})^{\alpha}[/itex]

    This is a problem. I don't see how else to solve this problem.

    .105 = F(1) - F(0)
    .641 = 1- [F(2) - F(0)]

    Thanks for any help.
  2. jcsd
  3. Apr 8, 2013 #2

    Ray Vickson

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    Science Advisor
    Homework Helper

    Do you know what F(x) is actually supposed to represent? How would that relate to the given data? In particular, what are the values of x for your given data?

    Note: to avoid confusion, make a distinction between X (a random variable) and x (a possible numerical value of X). These are NOT the same. So, your given data are
    [tex] P(X \leq 1) = 0.105 \;\text{ and } P(2 \leq X) = P(X \geq 2) = 0.641.[/tex]
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