Question: 1. Given a random sample { X7, Xs,..., X, } of size n from an exponential pop- ulation with a probability density function 1,-3 .

1. Given a random sample { X7, Xs,..., X, } of size n from an exponential pop- ulation with a probability density function 1,-3 . f(w)={ '\\eofj e, otherwise. Let A be the maximum likelihood estimator of \\. (a) Find \\. (b) Show that A is an unbiased estimator of \\. (c) Find the Fisher information per observation about A. (d) Show that A is a minimum variance unbiased estimator of . (e) Show that A is a consistent estimator of \\. (f) Describe the limiting distribution of

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