[All Steps] Suppose that X_1, ... X_n is a random sample from a population with mean μ and unknown variance σ^2. That is E(X_i)=μ and V(X_i)=σ^2
Question: Suppose that \(X_{1}, \ldots X_{n}\) is a random sample from a population with mean \(\mu\) and unknown variance \(\sigma^{2}\). That is \(E\left(X_{i}\right)=\mu\) and \(V\left(X_{i}\right)=\sigma^{2}\) for each \(\mathrm{i}\).
Prove that \(V(\bar{X})=\frac{\sigma^{2}}{n}\).
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