2. Let S2 Ei=1(X₁-X) ² be the sample variance of a random sample X₁, , Xn from a distribution with mean and variance o2 > 0. n-1 (a) Show that E(S²) = 0² (b) Show that S2 converges in Probability to 2

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2. Let S2 =
Σ=1(X₂-X)²
n-1
be the sample variance of a random sample X₁,..., Xn from a distribution with
mean and variance o² > 0.
(a) Show that E(S²) = 0²
(b) Show that S² converges in Probability to o2
Transcribed Image Text:2. Let S2 = Σ=1(X₂-X)² n-1 be the sample variance of a random sample X₁,..., Xn from a distribution with mean and variance o² > 0. (a) Show that E(S²) = 0² (b) Show that S² converges in Probability to o2
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