1. The following is an estimate of the population variance ?Ā²: 1 / (2(n - 1)) ?_{i=1}^{n-1} (x_{i+1} - x_i)Ā² (a) Prove that the above estimate is unbiased. (b) What is the advantage of this estimate compared to SĀ²? 2. As an estimate for variance the following statistic was used C ?_{i=1}^{n-1} (x_{i+1} - x_i)Ā² (a) If the estimate is unbiased, what is the value of the constant C? (b) What is the advantage of the suggested estimate compared to SĀ²?
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Step 1: To prove that the estimate (Ī£(Ti - TĢ)^2) / 2(n - 1) is unbiased, we need to show that the expected value of the estimate is equal to the population variance Ļ^2. Show moreā¦
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