5.34. Jones figures that the total number of thousands of miles that a racing auto can be driven before it would need to be junked is an1Smith has a used car that he claims has been driven only 10,000 miles. If Jones purchases theexponential random variable with parameter20car, 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 ofthe car is not exponentially distributed, but rather is (in thousands of miles) uniformly distributed over (0, 40)

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Asked Nov 21, 2019
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5.34. Jones figures that the total number of thousands of miles that a racing auto can be driven before it would need to be junked is an
1
Smith has a used car that he claims has been driven only 10,000 miles. If Jones purchases the
exponential random variable with parameter
20
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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5.34. Jones figures that the total number of thousands of miles that a racing auto can be driven before it would need to be junked is an 1 Smith has a used car that he claims has been driven only 10,000 miles. If Jones purchases the exponential random variable with parameter 20 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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Expert Answer

Step 1

Lack of memory property:

Let the random variable X is exponentially distributed with parameter 1/λ. It is known that X> t. The lack of memory property states that P(X > s+t | X > t) = P(X > s).

Step 2

Calculations:

It is given that the total number of thousands of miles that a racing auto can be driven before it would be junked is an exponential distribution with parameter 1/20.  The car has been driven 10,000 miles. The random variable X denotes the total number o...

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P(X2 20,000 10,000 | X>10,000)- P(X2 20,000) 1 dx 20 20 1 20 1 20 =e =0.3679 8

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