GATE Estimation: Unbiased and Minimum Variance Estimation – Previous Year Questions
11 GATE previous year questions on Unbiased and Minimum Variance Estimation (Estimation, Statistics) with answers and explanations, from every paper.
- GATE 2021 ST Q49 – X₁,…,X n are iid exponential with mean θ>0,n≥2. Let X (1)=min X i and T=ΣX i. Find E(X (1) T).
- GATE 2022 ST Q55 – The Poisson(θ) sample is 0,1,1,2,0. If α is the minimum-variance unbiased estimate of P(X≤1),find 5⁴α as an integer.
- GATE 2022 ST Q59 – A gamma density is x⁴e(−x/β)/(24β⁵),x>0,β>0. For β=2,find the Cramér–Rao lower bound for variance of an unbiased estimator of β² from n=8…
- GATE 2023 ST Q24 – For an iid size-n sample from Uniform(1/3,θ),θ>1/3,let Y=max X i. Which estimator of θ is unbiased?
- GATE 2023 ST Q63 – The observations −1,−1/2,1,5/2,3 form a sample of size 5 from N(1/2,σ²),σ>0 unknown. T is an unbiased estimator of σ² attaining the Cramér–Rao lower…
- GATE 2024 ST Q54 – An iid Poisson(λ) sample n≥2 defines T₁=X̄ and T₂=√[Σ(X i−X̄)²/(n−1)]. Which hold?
- GATE 2024 ST Q55 – For iid Bernoulli(p) X₁,X₂,X₃, define T₁(X i,X j,X k)=X i−X j(1−X k) and T₂(X i,X j,X k)=(X iX j+X jX k)/2 for distinct indices. Which hold?
- GATE 2025 ST Q33 – Five observations are iid N(θ,6),θ∈ℝ. Let c(θ) be the Cramér–Rao variance bound for unbiased estimation of θ. Find 15inf (θ∈ℝ)c(θ) (integer).
- GATE 2025 ST Q52 – An iid sample is uniform on (−θ/2,θ/2),θ>0. Which hold?
- GATE 2026 ST Q20 – X₁,X₂ are independent N(θ,1),θ∈ℝ. Which listed statistic attains the Cramér–Rao lower bound for estimating its own expected value?
- GATE 2026 ST Q64 – X₁,X₂ are iid uniform(0,θ),θ>0, with maximum T=X (2). Let ψ(θ)=P θ(X₁+X₂<1). A continuous δ:(0,∞)→ℝ makes δ(T) an unbiased estimator of ψ(θ) for every…