Survival times have the exponential distribution with pdf (x; ) = e x for x 0,

Survival times have the exponential distribution with pdf ƒ(x; λ) = λe ^–λx for x ≥  0, where λ > 0 is unknown. However, we wish to estimate the mean μ = 1/λ based on the random sample X₁, X₂, …, X_n, so let’s re-express the pdf in the form (1/μ)e^–x/μ.
a. Find the information in a single observation and the Cramér–Rao lower bound.
b. Determine the mle of μ.
c. Find the mean and variance of the mle.
d. Is the mle an efficient estimator? Explain.