Let Y1 be the smallest observation of three independent random variables W1, W2, W3

Chapter 3, Problem 3.4-3

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Let Y1 be the smallest observation of three independent random variables W1, W2, W3, each with a Weibull distribution with parameters and . Show that Y1 has a Weibull distribution. What are the parameters of this latter distribution? Hint: G(y1) = P(Y1 y1) = 1 P(y1 < Wi, i = 1, 2, 3) = 1 [P(y1 < W1)]3.

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