Continuous-Time Memorylessness

EasyProbability

Let $X \sim \text{Exp}(\lambda)$ and $s,t \geq 0$ be fixed real numbers. Compute $\mathbb{P}[X > s + t \mid X > t]$ . Report the answer when $\lambda = 1, t = 3,$ and $s = 2$ to the nearest thousandth.

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