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📐 Mathematics  ·  Probability  ·  JEE

Random variable X has E[X] = 3 and E[X²] = 13. Variance of X =

Answer: 4.

  • A 4
  • B 10
  • C 9
  • D 16

Correct answer: A. 4

Explanation: Variance formula: Var(X) = E[X²] − (E[X])². Substituting: Var(X) = 13 − 3² = 13 − 9 = 4. Standard deviation SD = √4 = 2. This is the shortcut form avoiding direct computation of Σ(xᵢ−μ)²p(xᵢ).

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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