Mean Residence Time Calculation for a given system:
\[
t_m = \int_0^{\infty} t E(t) \, dt
\]
Where \( E(t) \) is the distribution function.
For the given system, the distribution function is:
\[
E(t) = 1 - 2t, \quad t \leq 0.5
\]
\[
E(t) = 0, \quad t > 0.5
\]