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Xˉ∼N(μ,σ2n)\bar{X} \sim N(\mu, \frac{\sigma^2}{n})Xˉ∼N(μ,nσ2)
Exact for normal populations; approximate for non-normal with large n
n≥25n \geq 25n≥25
For non-normal or unknown distributions with large n
σ2n\frac{\sigma^2}{n}nσ2
Use s2s^2s2 (sample variance)
E(Y)=∑y⋅P(Y=y)E(Y) = \sum y \cdot P(Y=y)E(Y)=∑y⋅P(Y=y)
E(Y2)=∑y2⋅P(Y=y)E(Y^2) = \sum y^2 \cdot P(Y=y)E(Y2)=∑y2⋅P(Y=y)
Var(Y)=E(Y2)−[E(Y)]2\text{Var}(Y) = E(Y^2) - [E(Y)]^2Var(Y)=E(Y2)−[E(Y)]2
1n\frac{1}{n}n1
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