Problem Suppose that X;, i= 1, ., n, are iid Bernoulli(p). (a) Show that the variance of the MLE of p attains the Cramér-Rao Lower Bound. (b) For nz 4, show that the product X,X2X3X4 is an unbiased...

Problem<br>Suppose that X;, i= 1, ., n, are iid Bernoulli(p).<br>(a) Show that the variance of the MLE of p attains the Cramér-Rao Lower Bound.<br>(b) For nz 4, show that the product X,X2X3X4 is an unbiased estimator of p, and use this fact<br>to find the best unbiased estimator of p4.<br>

Extracted text: Problem Suppose that X;, i= 1, ., n, are iid Bernoulli(p). (a) Show that the variance of the MLE of p attains the Cramér-Rao Lower Bound. (b) For nz 4, show that the product X,X2X3X4 is an unbiased estimator of p, and use this fact to find the best unbiased estimator of p4.

Jun 11, 2022

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Problem Suppose that X;, i= 1, ., n, are iid Bernoulli(p). (a) Show that the variance of the MLE of p attains the Cramér-Rao Lower Bound. (b) For nz 4, show that the product X,X2X3X4 is an unbiased...

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