Rao-Blackwell for p Squared
Four independent Bernoulli trials with success probability p = 1/2 are observed, X₁, ..., X₄. The crude estimator X₁X₂ is unbiased for p². Let T = X₁ + X₂ + X₃ + X₄ be the total number of successes, which is sufficient for p, and let W = E[X₁X₂ | T] be the Rao-Blackwellised estimator. Find Var(W) when p = 1/2. Give a reduced fraction.
Related problems & prerequisites
Worth solving first
- Variance of Two Dice 2.0/10
Source: Original problem written for AxiomIQ, applying the Rao-Blackwell theorem.