GATE Estimation: Sufficiency and Completeness – Previous Year Questions
7 GATE previous year questions on Sufficiency and Completeness (Estimation, Statistics) with answers and explanations, from every paper.
- GATE 2021 ST Q50 – For an iid size-n sample from Uniform(0,θ),θ>0,n≥2,let X (1),X (n) be the extremes. P:(X (1),X (n)) is complete. Q:the range X (n)−X (1) is ancillary.…
- GATE 2022 ST Q19 – For an iid sample of size n from f(x;θ),which statement is NOT true?
- GATE 2024 ST Q23 – Independent X₁,X₂,X₃ are Binomial(100,p),0<p<1 unknown. Let T₁=(X₁+X₂,X₃),T₂=X₁+X₂+X₃. I:T₂ T₁ has a parameter-free distribution. II:T₁ T₂ has a…
- GATE 2025 ST Q18 – T is complete sufficient for a family of distributions, U is sufficient, and T≥0 almost surely under every member. Which is not necessarily true?
- GATE 2025 ST Q42 – An iid sample n≥2 is N(−θ,θ), with θ>0 unknown. Which holds?
- GATE 2026 ST Q19 – A sample X₁,X₂ has density f α(x)=αx(α−1)e(−xα),x>0, zero otherwise,α>0 unknown. Let X (1)=min(X₁,X₂),X (2)=max(X₁,X₂). Which statement is correct?
- GATE 2026 ST Q43 – An iid sample of size 3 has P θ(X i=1)=θ,P θ(X i=2)=1−θ,0<θ<1. Which statistic is not sufficient?