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34. Jones figures that the total number of thousands of miles that an auto can be driven before it would need to be junked as an exponential random variable with parameter 1/20. Smith has a used car that he claims has been driven only 10,000 miles. If Jones purchases the car, what is the probability that she would get at least 20,000 additional miles out of it? Repeat under the assumption that the lifetime mileage of the car is not exponentially distributed but rather is (in thousands of miles) uniformly distributed over (0, 40).

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X is a exponential random variable with parameter b if its probability density function is given by
f(x) = b*EXP(-bx)
The cumulative distribution function (CDF) of an exponential random ...

Solution Summary

This shows how to calculate probabilities with exponential and uniform distribution.