a) Let X₁, X₂, X, denote a random sample from N (0,02) distribution with probability density function: 1 O√2π And let S² = be the estimator of o². i) Show whether or not that S² is an unbiased estimator of o²? ii) Show that S² is a consistent estimator of o². f(x; σ²) = Σ',xp n e 20² -0

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a) Let X₁, X2,..., Xn denote a random sample from N(0, 2) distribution with
probability density function:
f(x; σ²)
=
1
O√2π
x²
e 20² -∞0 < x < 00
And let S² = Σ1x7
be the estimator of ².
n
i) Show whether or not that S² is an unbiased estimator of o²?
ii) Show that S² is a consistent estimator of o².
Transcribed Image Text:a) Let X₁, X2,..., Xn denote a random sample from N(0, 2) distribution with probability density function: f(x; σ²) = 1 O√2π x² e 20² -∞0 < x < 00 And let S² = Σ1x7 be the estimator of ². n i) Show whether or not that S² is an unbiased estimator of o²? ii) Show that S² is a consistent estimator of o².
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X~N(0, standard deviations σ2)

 

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