Mixture of exponentials suppose that a population contains, Ask an Expert

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Mixture of exponentials. Suppose that a population contains a proportion p of units from an exponential life distribution with mean θ, and the remaining proportion 1 -p from an exponential life distribution with mean θ,. Proschan (1963) treats such a problem.

(a) Derive the hazard function of the mixture distribution.
(b) Show that the failure rate of the mixture distribution decreases with age.

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