Suppose X_1,\ldots,X_n is a random sample
from an \text{Exponential}(\lambda) distribution.
Let \bar{x} denote the mean of this sample.
If n=25 and \bar{x}=6.2,
a)
What is \lambda, the m.l.e. for
\hat{\lambda}?
\hat{\lambda} = \input \text{(to $2$ decimal places)}
b)
Calculate an estimate of the expected information I(\lambda)
I(\lambda) = \input \text{(to $2$ decimal places)}
c)
Calculate a 99.9% confidence interval
(a,b) for \lambda:
\begin{multline}
a = \input \text{(to $2$ decimal places)} \\
b = \input \text{(to $2$ decimal places)} \\
\end{multline}