Mathematics · Probability and Statistics
One million random numbers are generated from a statistically stationary process with a Gaussian distribution having mean zero and variance σ02. The variance is estimated by randomly drawing a sample of 10,000 numbers (xn). Two estimators, σ̂12 and σ̂22, are computed as follows: σ̂12 = 110000 ∑n=110000 xn2 and σ̂22 = 19999 ∑n=110000 xn2. Which of the following expressions regarding their expected values is true?
Verified Solution4 OptionsUpdated: October 2026👁️1 View
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- 1E(σ̂22) = σ02
- 2E(σ̂2) = σ0
- 3E(σ̂12) = σ02✓
- 4E(σ̂1) = σ̂2
Correct answer
E(σ̂12) = σ02
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