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# iid Estimating variance for normal data. Suppose that we observe data X1, ..., Xn N(0, v) we know the mean is 0, but we

## iid Estimating variance for normal data. Suppose that we observe data X1, ..., Xn N(0, v) we know the mean is 0, but we don't know the variance v. (We are writing variance = v, instead of , to make it clear that we are working with variance rather than with standard deviation as our parameter.) (a) Calculate the MLE estimate for vas a function of the data X1, ..., Xn. (b) Calculate the Fisher information I(v). (c) Calculate the approximate normal distribution of the MLE , if the true variance is v and the sample size n is large. (The mean and variance of the normal may depend on n and/or vo, but should not depend on any other quantities.)

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