1. MLE of the Exponential Rate For n > 1, let X1, X2, ..., X, be...

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1. MLE of the Exponential Rate For n > 1, let X1, X2, ..., X, be i.i.d. exponential (^) variables. n a) Let ,, be the maximum likelihood estimate (MLE) of the parameter A. Find , in terms of the sample mean X = X. The subscript n in X, is there to remind us that we have the average of n values. It doesn't refer to the nth sampled value X. b) Use facts about sums and linear transformations to find the distribution of X, with little or no calculation. Recognize it as one of the famous ones and provide its name and parameters. Use it to find E(). c) Is, an unbiased estimate of 1? If it is biased, does it overestimate on average, or does it underestimate? Is it asymptotically unbiased? That is, does E() converge to as n co? ewpage 1. MLE of the Exponential Rate For n > 1, let X1, X2, ..., X, be i.i.d. exponential (^) variables. n a) Let ,, be the maximum likelihood estimate (MLE) of the parameter A. Find , in terms of the sample mean X = X. The subscript n in X, is there to remind us that we have the average of n values. It doesn't refer to the nth sampled value X. b) Use facts about sums and linear transformations to find the distribution of X, with little or no calculation. Recognize it as one of the famous ones and provide its name and parameters. Use it to find E(). c) Is, an unbiased estimate of 1? If it is biased, does it overestimate on average, or does it underestimate? Is it asymptotically unbiased? That is, does E() converge to as n co? ewpage