The GATE Grind

GATE Joint Distributions: Sampling Distributions – Previous Year Questions

2 GATE previous year questions on Sampling Distributions (Joint Distributions, Statistics) with answers and explanations, from every paper.

  1. GATE 2022 ST Q43 (2 marks, Multiple choice) – X₁,…,X₇ are iid N(0,θ),θ>0. Set K=(X₁²+X₂²)/Σ (i=1)7X i². I:K and ΣX i² are independent. II:7K/2∼F (2,7). III:E K²=8/63. Which hold?
  2. GATE 2025 ST Q49 (2 marks, Multiple select) – Independent standard normal X₁,X₂,X₃ define Y₁=X₁−X₂,Y₂=X₁+X₂−2X₃,Y₃=X₁+X₂+X₃. Which hold?