3. If a random variable X has a chi square distribution with v degrees of freedom, then E(X)= vand Var (X) = 2v. Let X₁, X₂,..., X be a random sample from a N (u, o2) distribution and let 5² = ²₁ (₁-x)² and 5² = (X-X)² be two estimators of o². - n-1 n b) Find the Mean square error of ²

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3. If a random variable X has a chi square distribution with v degrees of freedom,
then E(X)= v and Var (X) = 2v.
Let X₁, X₂,..., X be a random sample from a N (u, o2) distribution and let
5² = [²=1(x₁-x)² and 5² = ²-₁(X₁-X)² be two estimators of o².
n-1
n
b) Find the Mean square error
of 5².
Transcribed Image Text:3. If a random variable X has a chi square distribution with v degrees of freedom, then E(X)= v and Var (X) = 2v. Let X₁, X₂,..., X be a random sample from a N (u, o2) distribution and let 5² = [²=1(x₁-x)² and 5² = ²-₁(X₁-X)² be two estimators of o². n-1 n b) Find the Mean square error of 5².
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E(X)=v, V(X)=2V 


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