GATE DA Practice Questions - GATE Data Science And Artificial Intelligence (DA) Exam

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Which of the following best describes the central limit theorem (CLT) for an i.i.d. sample of size n from a distribution with finite mean μ and variance σ²?

The sample mean converges to μ as n → ∞ in probability, regardless of the underlying distribution shape The standardized sample mean (X̄ − μ)/(σ/√n) converges in distribution to N(0,1) as n → ∞ The sample variance is always normally distributed for large n The original distribution becomes normal as n increases

Correct Answer:

The standardized sample mean (X̄ − μ)/(σ/√n) converges in distribution to N(0,1) as n → ∞

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