I am finding the value of rate parameter but unfortunately I am confused to get it. The question is in below:
I am solving an exponential distribution question and I am confused with the given rate parameter. The exponential distribution question is in below:
Suppose that the lifetime $X$ of a fuse (in 100 hour units) is exponentially distributed with $P(X>10)=0.8$. Find the rate parameter.
As I understand for this question:
$$\begin{align} P(X>10) = 0.8\\ 0.8 = e^{-\lambda 10} \end{align} $$
Here I am confused to substitute lambda aside to calculate it. May I know how can I substitute lambda aside to calculate lambda value? Or do I interpret correctly to find the rate parameter?