5.2.30

Suppose that the number of years a car will run is exponentially distributed with parameter ยต = 1/4. If Prosser buys a used car today, what is the probability that it will still run after 4 years?

In this case the probablity the car breaks down within 4 years is \(P(T\leq x) = 1 - e^{-\frac{1}{4}x}\), according to the reading. To get the probablity that the car still runs after four years is the compliment of this probabilty: \(P(T > 4) = e^{-\frac{1}{4}4}\) , such that \(P = e^{-1} = 0.3678794\)

exp(-1)
## [1] 0.3678794