Math Solutions

[All Steps] Let T = minX 1 , X 2 , X 3 , where each Xi ~ Weibull(,) and X1, X2, X3 are independent (component lifetimes). Show that T also has a Weibull

Question: Let T = min{X 1 , X 2 , X 3 }, where each Xi ~ Weibull(,) and X1, X2, X3 are independent (component lifetimes). Show that T also has a Weibull distribution exactly with some shape and scale parameters. (This is the so-called "weakest-link model." Hint: Find the reliability function of T.)

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