Suppose that Θ , 𝑋1 , and 𝑋2 have zero means. Furthermore,

Question

𝖵𝖺𝗋(𝑋1)=𝖵𝖺𝗋(𝑋2)=𝖵𝖺𝗋(Θ)=4,

and

𝖢𝗈𝗏(Θ,𝑋1)=𝖢𝗈𝗏(Θ,𝑋2)=𝖢𝗈𝗏(𝑋1,𝑋2)=1.

The LLMS estimator of Θ based on 𝑋1 and 𝑋2 is of the form Θˆ=𝑎1𝑋1+𝑎2𝑋2+𝑏 . Find the coefficients 𝑎1 , 𝑎2 , and 𝑏 . Hint: To find 𝑏 , recall the argument we used for the case of a single observation.

Answer 1

stop trying to disguise a homework dump by using different names.

As you may have guessed, the expertise level on statistics is a bit low here on this site. I had my one statistics class almost 50 years ago, so I'd have to study the subject again to answer these questions you post.

Clearly, it looks like you will have to do the same.

Answer 2

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You are welcome!