A memoryless component

Topic: Random variables and distributions · more questions on this topic
‹ Groups of three Why a normal variance is \sigma^2 ›

A component has an exponential lifetime with expectation 2 years.

1. Find the probability that it still works after 2 years.

2. Find the probability that it still works after 10 years, given that it still works after 7 years.

Worked answer (click to show)

The mean is 2, so the rate is \lambda=1/2.

1. \mathbb{P}(X>2)=e^{-1}\approx 0.368.

2. Memorylessness gives \mathbb{P}(X>10\mid X>7)=\mathbb{P}(X>3)=e^{-3/2}\approx 0.223.