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📐 Mathematics  ·  Probability  ·  JEE

The strong law of large numbers states:

Answer: Sample mean converges almost surely to population mean.

  • A Sample mean converges in probability to population mean
  • B Sample mean converges almost surely to population mean
  • C Sample variance is generally assumed correct without further checking
  • D This applies mainly to normal distributions specifically

Correct answer: B. Sample mean converges almost surely to population mean

Explanation: Strong LLN: sample mean converges almost surely (with probability 1) to expected value. Stronger than weak LLN (convergence in probability).

UABA and BA onlyB onlyOutside both circles: complement of (A union B)

Venn diagram of the universal set U with events A and B, showing the intersection (A and B), the parts unique to each event, and the complement region outside both.

Concept context

Chance, events, conditional probability, and Bayes theorem

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