A non-negative loss in a car accident is distributed with the following probability density function
\[
f(x)=\frac{1}{10} \exp (-x / 10)
\]
for $x \geq 0$. Suppose that first $5$ units of loss is incurred by the insured and the remaining loss if any is covered by the insurance company. What is the expected loss to the insurance company?
- $10 \exp \left(-\frac{1}{2}\right)$
- $10$
- $5 \exp \left(-\frac{1}{2}\right)$
- $5+10 \exp \left(-\frac{1}{2}\right)$
- $15 \exp \left(-\frac{1}{2}\right)$