Anu reached a bus stop at $\text{9:00 AM.}$ She knows that the number of minutes after $\text{9:00 AM}$ when the bus will arrive is distributed with probability density function (p.d.f.) $f$ where
\[f(x)=\frac{1}{10} \exp (-x / 10)\]
for $x \geq 0$, and $f(x)=0$ for $x<0$.
At $\text{9:05 AM,}$ the bus had still not arrived. Given her knowledge of this fact and of the p.d.f. $f$ of the arrival time of the bus, at what time, measured in minutes after $\text{9:00 AM,}$ would Anu expect the bus to arrive?
- $12.5$
- $15$
- $7.5$
- $10$
- $12.5$
