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### quiz6dsol

Course: SMAM 351, Fall 2009
School: RIT
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Word Count: 205

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351 Quiz SMAM 6 d Name_______ 1. The exponential probability density function below of random variable T represents the time until a machine part fails in years. .2e -.2t g(t) = 0 t&gt;0 elsewhere A. What is the mean time before failure? (2 points) 1/.2 = 5 years B. A part has been in operation for 5 years? What is the probability that it fails before the end of the ten years? (4 points) P(T 10| T...

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351 Quiz SMAM 6 d Name_______ 1. The exponential probability density function below of random variable T represents the time until a machine part fails in years. .2e -.2t g(t) = 0 t>0 elsewhere A. What is the mean time before failure? (2 points) 1/.2 = 5 years B. A part has been in operation for 5 years? What is the probability that it fails before the end of the ten years? (4 points) P(T 10| T > 5) = .2e -.2x dx = 1-e -.2x 0 = 1- e -1 = .632 0 5 5 C. What is the median failure time of such parts? (4 points) ..2e t 0 -.2x dx = .5 1- e-.2t = .5 e-..2t = .5 -.2t = ln(.5) t = -5ln(.5) = 3.46yrs 2. A random variable X is said to have Weibull a distribution if the probability density function is x - 1e -(x/ ) x 0 f(x;,) = 0 x <0 The cumulative distribution function is 0 x<0 F(x;,) = - (x/ ) x 0 1- e The lifetime X in hundreds of hours has a Weibull distribution with parameters = 2, = 7 . A. What is the probability that the life of the part is between 300 and 500 hours? (5 points) F(5,2,7) -F(3,2,7)...

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