2. Let X represents the lifetime of water turbine in years. The lifetime of the turbine is a random variable withthe following pdff(x) = ke-0.5x, X>0a. Find k.b. Find the probability that the turbine will be operational for 2 years.c. Find the probability that the turbine will break down after 8 months.

Answered: 2. Let X represents the lifetime of…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Suppose that the length X of the life (in years) of a battery for a computer has a distribution that can be described by the pdf: f(x) = e 121 Determine the probability that the battery fails before the one year warranty expires on the computer. e one
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Assume that there is a rare disease. It occurs in the population at a rate of 1 per 1000; that is, P[disease] = 0.001. There is a test for the disease that has an error rate of 5% for in positive and negative senses. That is, if a patient has the disease, there is 95% probability that the test will confirm that status and 5% probability that the test will be negative. Conversely, if the patient does not have the disease, there is 5% probability that the test will indicate erroneously that the disease is present and 95% probability that the test will confirm that the disease is not present. Let PT indicate a positive test, D indicate the disease is present, and a bar over a symbol indicates the negative, so this can all be summarized as Po(D) = 0.001 P(PT|D) = 0.95 P(PT|D) = 0.95 P(PT|D) = 0.05 P(PT|D) = 0.05 The disease is serious, and the treatment is difficult and expensive, so a decision either to treat or not to treat the disease is not trivial. A patient takes the test and…
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