Let X₁,..., XN be a simple random sample from a N(μ, o²) population. For any constant k > 0, N define ô² = (²1(X₁ — X)²)/k. Consider of as an estimator of o². - To provide numerical answers (but not for your working), use the values N = 6, o² = 8, k = 3. For part (d) use your calculated value of k rather than this one.)

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Compute the bias of ô2 in terms of k.
Compute the variance of ô in terms of k.
Compute the mean squared error of ô in terms of k.
Transcribed Image Text:Compute the bias of ô2 in terms of k. Compute the variance of ô in terms of k. Compute the mean squared error of ô in terms of k.
Let X₁,..., XN be a simple random sample from a N(μ, σ²) population. For any constant k > 0,
define ô² = ([~1(X¡ – X)²)/k. Consider of as an estimator of o².
To provide numerical answers (but not for your working), use the values N = 6, o² = 8, k = 3.
For part (d) use your calculated value of k rather than this one.)
Transcribed Image Text:Let X₁,..., XN be a simple random sample from a N(μ, σ²) population. For any constant k > 0, define ô² = ([~1(X¡ – X)²)/k. Consider of as an estimator of o². To provide numerical answers (but not for your working), use the values N = 6, o² = 8, k = 3. For part (d) use your calculated value of k rather than this one.)
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