X1,...,Xn are IID with N(0,2). a) Determine the mean and variance for (X (subscript 1)^2) b)...

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Question

X₁,...,X_n are IID with N(0, $\sigma$ ²).

a) Determine the mean and variance for (X (subscript 1)^2)

b) Show

$√ n [ log ( 1 n ∑n i=1 X2 i ) − log(σ 2 ) ] d → N(0, 2).$ sqrt(n) * [ log ( 1/n ∑(from i=1 to n) X_i²) − log(σ² ) ] d → N(0, 2).

math Statistics-And-Probability

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