Under the same assumptions as question 16a, and using the fact that $\mu$ is constant (question 15b) and that $\int_0^{+\infty} g_0(t)\,dt = \mathbb{E}(X)$, deduce that $\mu(t) = \dfrac{1}{\mathbb{E}(X)}$ for all $t \geqslant 0$.
Under the same assumptions as question 16a, and using the fact that $\mu$ is constant (question 15b) and that $\int_0^{+\infty} g_0(t)\,dt = \mathbb{E}(X)$, deduce that $\mu(t) = \dfrac{1}{\mathbb{E}(X)}$ for all $t \geqslant 0$.