Solution
= Solution
Condition on the bulb being alive at age $\tau$. The next hour's survival <likelihood contribution> is
$$
\frac{F(\tau+1)}{F(\tau)}
=\frac{e^{-\lambda(\tau+1)}}{e^{-\lambda\tau}}
=\boxed{e^{-\lambda}}.
$$
\b[It does not depend on the unknown age] $\tau$. This is <memorylessness of the exponential distribution>: the residual lifetime given survival has the same <exponential distribution> as a new lifetime.