Let the life W (in years) of the usual family car have a Weibull distribution with = 2

Chapter 3, Problem 3.4-1

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QUESTION:

Let the life W (in years) of the usual family car have a Weibull distribution with\(\alpha = 2\). Show that \(\beta\) must equal 10 for \(P(W>5)=e^{-1 / 4} \approx 0.7788\). Hint: \(P(W > 5) = e^{−H(5)}\).

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QUESTION:

Let the life W (in years) of the usual family car have a Weibull distribution with\(\alpha = 2\). Show that \(\beta\) must equal 10 for \(P(W>5)=e^{-1 / 4} \approx 0.7788\). Hint: \(P(W > 5) = e^{−H(5)}\).

ANSWER:

Step 1 of 3

Given  has a Weibull distribution with

pdf of a Weibull distribution:

Replace  by 2

The cdf at  is the integral of the pdf up to  :

Let  and .

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