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Question: in some applications a sample of failure times comes from...

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Problem 2: In some applications, a sample of failure times comes from a mixture of subpopulations. (a) Write down the expression for the CDF, PDF, and reliability function for a mixture of two cxponential distributions with rates Mi and 12 (subpopulations 1 and 2. respectively) and p being the proportion from subpopulation 1. Mi M2 (b) What is the shape of the hazard rate function and prove that the mixture of two exponential distributions with different rate parameters always has that shape. (c) Find the MTTFof the mixture of two exponential distributions.
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