Variance of the Sample Variance of Dice
Three fair six-sided dice are rolled independently. Let S² = (1/2) Σ (Xᵢ − X̄)² be the usual sample variance with the n − 1 denominator. Find Var(S²) exactly, as a reduced fraction.
Related problems & prerequisites
Worth solving first
Source: Original problem written for AxiomIQ; uses the exact fourth-moment formula for Var(S²).