How can I calculate $E(\max${T,$5$}$)$ while $ T\sim \exp(\frac{1}{30}) $?

Question

How can I calculate $E(\max${T,$5$}$)$ while $ T\sim\exp(\frac{1}{30}) $ ?

Answer 1

Guide:

A little push to get you started:

Evaluate $$\int_0^\infty \max(t,5) f_T(t) \, dt$$

Note that $\max(t,5) =\begin{cases} 5 &, t\le 5 \\ t &, t>5\end{cases}$

You might like to split your integral up according to whether $t$ is bigger than $5$.