Question

The random variable X is exponentially distributed with mean 3. Find P(X > t + 3|X > t)
where t is any positive real number.

Answer 1

Gicen $X\sim Exp(\lambda), \mu=3$

$$\lambda=\dfrac{1}{\mu}=\dfrac{1}{3}$$

By the Memoryless Property:

$$P(X>t+r|X>t)=P(X>r), r\geq0, t\geq0$$

Then

$$P(X>t+3|X>t)=P(X>3)$$

$$=e^{-3({1 \over 3})}=e^{-1}\approx0.3679$$