Let \sigma =1 and consider the special case of only two observations (n=2). Write down a formula for the mean squared error \mathbb {E}[(\hat{\Theta }_1-\Theta _1)^2], as a function of t_1 and t_2. Enter t_1 for t_1 and t_2 for t_2.

Question

\mathbb {E}[(\hat{\Theta }_1-\Theta _1)^2]=\quad
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Consider the "experimental design" problem of choosing when to make measurements. Under the assumptions of the previous part, and under the constraints 0\leq t_1,t_2 \leq 10, find the values of t_1 and t_2 that minimize the mean squared error associated with the MAP estimator.

t_1=\quad
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t_2=\quad

Answer 1

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