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GATE Electrical Engineering (EE) 2023 Solved Paper

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Question : 25

Total: 65

One million random numbers are generated from a statistically stationary process with a Gaussian distribution with mean zero and standard deviation 𝜎₀.
The 𝜎₀ is estimated by randomly drawing out 10,000 numbers of samples (𝑥_𝑛). The estimates 𝜎̂₁, 𝜎̂₂ are computed in the following two ways.

Σn=110000xn2

E(
^
σ
22)=σ02
E(
^
σ
2)=σ0
E(
^
σ
12)=σ02
E(
^
σ
1)=
^
σ
2

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