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You know that there is a problem in your car due to sounds you hear when...

You know that there is a problem in your car due to sounds you hear when driving. There can be only two sources for the problem 1) Brakes 2) Engine. You are estimating that the problem is due to brakes with probability 0.6, and it is due to engine with probability 0.4. Furthermore, if the problem is due to brakes or engine, the number of miles you can drive without any repair is exponentially distributed with mean 500 and 100 miles, respectively.


a) What is the probability that the number of miles you can drive the car without any repair is larger than 200 miles.?


b) What is the expected number of miles you can drive the car without any repair?

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