GATE Estimation: Point Estimation and Consistency – Previous Year Questions
16 GATE previous year questions on Point Estimation and Consistency (Estimation, Statistics) with answers and explanations, from every paper.
- GATE 2021 ST Q13 – An iid sample of size n≥2 has density exp[−(x−θ)/θ]/θ for x>θ,zero otherwise,θ>0. Find the method-of-moments estimator of θ.
- GATE 2021 ST Q61 – The observations .90,.50,.01,.95 are iid with density [θ/(1−θ)]x[(2θ−1)/(1−θ)] on 0<x<1,where .5≤θ<1. Find the MLE of θ,to two decimals.
- GATE 2022 ST Q13 – S² is the sample variance with divisor n−1 from n>1 iid normal observations with unknown μ and σ²>0. I:S² is unbiased for σ² and S is unbiased for σ.…
- GATE 2022 ST Q33 – Four observations 6,5,3,6 come from density 2(θ−x)/θ² on 0<x<θ,zero elsewhere. Find the method-of-moments estimate of θ as an integer.
- GATE 2022 ST Q58 – An iid size-five sample from density 3x²/θ³ on 0<x<θ is 3,6,4,7,5. Find the MLE of the 1/8 quantile,to one decimal.
- GATE 2023 ST Q22 – X has exponential density e(−x/λ)/λ for x>0,λ>0 unknown. Y₁,…,Y n are iid with the distribution of X² and Ȳ is their mean. Which is the…
- GATE 2023 ST Q23 – An iid sample of size n≥2 has density f(x;θ)=2(−ln x) exp[−(ln x)²/θ]/(θx) on 0<x<1,zero otherwise,θ>0. Which expression is the MLE of θ?
- GATE 2023 ST Q39 – An iid sample of size n has density exp[−(x−μ)] for x≥μ,zero otherwise,μ unknown. Let M̂ be the MLE of the population median. Which holds when μ=1?
- GATE 2023 ST Q40 – X₁,…,X₁₀ are iid N(0,θ²),θ>0. Set T=ΣX i²/10. For c>0,the MSE of cT as an estimator of θ² is minimized at c₀. Find c₀.
- GATE 2024 ST Q24 – An iid sample n≥2 has density θ(2x)(θ−1) on 0<x≤1/2 and θ(2−2x)(θ−1) on 1/2<x≤1,zero otherwise,θ>0. Put L=Σ (X i≤1/2)ln(2X i)+Σ (X i>1/2)ln(2−2X i),…
- GATE 2024 ST Q44 – Independent X n~Poisson(λ+2(−n)),λ>0 unknown. Which holds?
- GATE 2024 ST Q62 – A Poisson process N(t) of unknown rate λ counts road potholes up to distance t km. Starting at zero, potholes occur at distances…
- GATE 2025 ST Q32 – Observed Bernoulli sample values are 0,1,1,1,0, with parameter θ∈(0,.7]. Find the MLE of θ to two decimals.
- GATE 2025 ST Q61 – Seven iid observations have density (λ³x²/2)e(−λx),x>0,λ>0 unknown. The MLE λ̂ has bias E(λ̂−λ)=αλ. Find 1/α (integer).
- GATE 2026 ST Q32 – A gamma sample has density λαx(α−1)e(−λx)/Γ(α),x>0, with unknown α,λ>0. The observed averages of x i and x i² are 2 and 5. Find the method-of-moments…
- GATE 2026 ST Q56 – An iid sample n≥2 has Laplace density e(− x−μ )/2,μ∈ℝ. Let μ̂ be an MLE and X̄ the sample mean. Which hold?