5. Let X1,..., X„ ~ iid N(0, T). (a) Find the MSE for the usual unbiased estimator of T: ↑ = 4E X?. Show that this is unbiased and find (X; - X)?. (b) Consider the alternative estimator 8(x) = E the...

5. Let X1,..., X„ ~ iid N(0, T).<br>(a) Find the MSE for the usual unbiased estimator of T:<br>↑ = 4E<br>X?. Show that this is unbiased and find<br>(X; - X)?.<br>(b) Consider the alternative estimator 8(x) = E<br>the MSE.<br>n Li=1<br>(c) Why does it make sense for (b) to be better than (a) in this case?<br>

Extracted text: 5. Let X1,..., X„ ~ iid N(0, T). (a) Find the MSE for the usual unbiased estimator of T: ↑ = 4E X?. Show that this is unbiased and find (X; - X)?. (b) Consider the alternative estimator 8(x) = E the MSE. n Li=1 (c) Why does it make sense for (b) to be better than (a) in this case?

Jun 08, 2022

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5. Let X1,..., X„ ~ iid N(0, T). (a) Find the MSE for the usual unbiased estimator of T: ↑ = 4E X?. Show that this is unbiased and find (X; - X)?. (b) Consider the alternative estimator 8(x) = E the...

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