# Exponential Distribution

• Mar 3rd 2013, 07:12 AM
wrexlive1
Exponential Distribution
For a certain type of electrical component, the lifetime X (in thousands of hours) has an Exponential
distribution with rate parameter lambda  = 0.5. What is the probability that a new component will last
longer than 1000 hours? If a component has already lasted 1000 hours, what is the probability that
it will last at least 1000 hours more?

Can anyone help with this question?
• Mar 3rd 2013, 11:06 AM
For (a) we are asked to calculate $P(X>1) = 1 - P(X<1)$ but we know what the CDF of a exponential distribution is, so
$P(X>1) = 1 - (1 - e^{-.5(1)} = e^{-.5} = .61$
For (b), we are asked to calculate $P(X>2|X>1) = \frac{P(X>2 and X>1)}{P(X>1)} = \frac{P(X>2)}{P(X>1)}$. I'll leave the rest up to you