The Weibull Distribution
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Questions and Answers

Which type of random variables does the Weibull distribution model?

  • Discrete random variables
  • Continuous random variables (correct)
  • Both discrete and continuous random variables
  • None of the above

    • Who is the mathematician after whom the Weibull distribution is named?

  • Maurice René Fréchet
  • Rosin & Rammler
  • Waloddi Weibull (correct)
  • None of the above

    • What is the probability density function of a Weibull random variable?

  • $f(x ; \lambda , k) = \frac{k},{\lambda} \left(\frac{x},{\lambda}\right)^{k-1} e^{-(x/\lambda)^k}$ (correct)
  • $f(x ; \lambda , k) = \frac{k},{\lambda} \left(\frac{x},{\lambda}\right)^{k+1} e^{-(x/\lambda)^k}$
  • $f(x ; \lambda , k) = \frac{\lambda},{k} \left(\frac{x},{\lambda}\right)^{k-1} e^{-(x/\lambda)^k}$
  • $f(x ; \lambda , k) = \frac{\lambda},{k} \left(\frac{x},{\lambda}\right)^{k+1} e^{-(x/\lambda)^k}$

    • What is the range of the Weibull random variable?

    <p>$[0, \infty)$</p> Signup and view all the answers

    Who first identified the Weibull distribution?

    <p>Rosin &amp; Rammler</p> Signup and view all the answers

    Which random variables does the Weibull distribution primarily model?

    <p>Continuous random variables</p> Signup and view all the answers

    What is the shape parameter of a Weibull random variable?

    <p>k</p> Signup and view all the answers

    What is the scale parameter of a Weibull random variable?

    <p>λ</p> Signup and view all the answers

    Which mathematician described the Weibull distribution in detail in 1939?

    <p>Waloddi Weibull</p> Signup and view all the answers

    What is the probability density function of a Weibull random variable?

    <p>$f(x; \lambda, k) = \frac{k},{\lambda}( \frac{x},{\lambda} )^{k-1}e^{-( \frac{x},{\lambda} )^k}$</p> Signup and view all the answers

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