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30. Show that a suitable power of a Weibull-distributed random variable whose parameter is gamma-distributed is Pareto-distributed. More pre- cisely, show that if X | A = a € W (₁, 1) with AET(p, 0), then X has a (translated) Pareto distribution.

30. Show that a suitable power of a Weibull-distributed random variable whose parameter is gamma-distributed is Pareto-distributed. More pre- cisely, show that if X | A = a € W (₁, 1) with AET(p, 0), then X has a (translated) Pareto distribution.

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter13: Probability And Calculus
Section13.2: Expected Value And Variance Of Continuous Random Variables
Problem 10E
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30. Show that a suitable power of a Weibull-distributed random variable whose parameter is gamma-distributed is Pareto-distributed. More pre- cisely, show that if X | A = a € W(,t) with A E r(p, 0) , then X has a (translated) Pareto distribution.
Transcribed Image Text:30. Show that a suitable power of a Weibull-distributed random variable whose parameter is gamma-distributed is Pareto-distributed. More pre- cisely, show that if X | A = a € W(,t) with A E r(p, 0) , then X has a (translated) Pareto distribution.
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