Suppose that the lifetime of an electronic component has exponential distribution with mean $100$ hours. Find the expected lifetime of the component, given that it has already been in use for $50$ hours.
Would someone please help me with this one?
This is what I got, ${\rm E}[X \mid X > c] = {\rm E}[X] + c = \frac{1}{\lambda} + c.$ Not sure if it's correct.
Yes, your solution is correct. The exponential distribution is memoryless so we have
$$E(X \mid X \gt 50)=50+E(X)$$