Let X1,..., Xn be iid exponential (). (a) Find an unbiased estimator of based only on

Let X1,..., Xn be iid exponential (λ).
(a) Find an unbiased estimator of λ based only on Y = min{X1,..., Xn}.
(b) Find a better estimator than the one in part (a). Prove that it is better.
(c) The following data are high-stress failure times (in hours) of Kevlar/epoxy spherical vessels used in a sustained pressure environment on the space shuttle:
50.1, 70.1, 137.0, 166.9, 170.5, 152.8, 80.5, 123.5, 112.6, 148.5, 160.0, 125.4.
Failure times are often modeled with the exponential distribution. Estimate the mean failure time using the estimators from parts (a) and (b).