Solution
= Solution
The <survival function> of this <exponential distribution> is $\mathbb P(X\geq t)=e^{-kt}$ for $t\geq0$. Since $\{X\geq3\}\subseteq\{X\geq1\}$, the <conditional probability> is
$$
\boxed{\mathbb P(X\geq3\mid X\geq1)=\frac{e^{-3k}}{e^{-k}}=e^{-2k}.}
$$
This is the <memoryless property>: after surviving the first unit, surviving two additional units has the same <probability> as it did initially.