### 5.2.30

Suppose that the number of years a car will run is exponentially distributed with parameter µ = 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