A fair six-sided die is rolled, with X being the number on the uppermost face. The variance of X is:

Question

Question

This question was previously asked in

SSC CGL Tier-II ( JSO ) 2019 Official Paper ( Held On : 17 Nov 2020 )

Answer 1

Formula

Variance X = σ²_x = E[(X – μ)²] = E(X²) – [E(X)]²

Calculation

E(X) = μ_x = μ

⇒ μ = ∑ x_if_i = ∑x_iP(X = x_j)

⇒ 1 × 1/6 + 2 × 1/6 + 3 × 1/6 + 4 × 1/6 + 5 × 1/6 + 6 × 1/6

⇒ (1/6)(1 + 2 + 3 + 4 + 5 + 6)

⇒ 7/2

E(X²) = ∑x_j²f(x_j) = ∑x_j²P(X = x_j)

⇒ 1² × 1/6 + 2² × 1/6 + ------6² × 1/6

⇒ 1/6(1² + 2² + 3² + 4² + 5² + 6²)

⇒ 1/6(1 +4 + 9 + 16 + 25 + 36)

⇒ 91/6

Variance X = E(X²) – [E(X)]²

⇒ 91/6 – (7/2)²

⇒ 91/6 – 49/4

∴ Variance X is 35/12

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