Studying for a mid-term, and not sure how to go about the following problem.
Given $t = 700$ as an average, I have to solve for lambda.
I'm thinking since t is determined, I don't need any integrals here, which would give
$$\lambda e^{-\lambda(700)} = .5$$
Assuming this is correct, I'm not sure how to solve for $\lambda$ since by taking the $ln$ I would put a $\lambda$ inside the $ln$.
If I have my formula wrong, then how would I go about solving it? I know I have an exponential distribution, and average "fail" time of 700, and I need to solve for $\lambda$. The rest of the information is just "story problem" story, but I can give it if necessary.
EDIT (Full Story problem):
Remi works at a large data center, and manages the hard drives for the servers. Assume that the probability density for a single hard drive failing after t days of use follows an exponential distribution. Remi observes that the average failure time for the hard drives is 700 days. Use this to determine $\lambda$.
The expected value, or average of a variable with exponential distribution is $\frac{1}{\lambda}$.