GATE Non-parametric Statistics: Empirical Distribution and Goodness of Fit – Previous Year Questions
8 GATE previous year questions on Empirical Distribution and Goodness of Fit (Non-parametric Statistics, Statistics) with answers and explanations, from every paper.
- GATE 2021 ST Q16 – A sample of 60 binary pairs gives counts n₁₁=10,n₁₀=20,n₀₁=20,n₀₀=10. Test independence of X,Y by Pearson’s chi-square test. Which statement gives the…
- GATE 2021 ST Q51 – X n are iid with CDF F. For real a<b,F(x)=0 on x≤a,0<F(x)<1 on a<x<b,and F(x)=1 on x≥b. Let S n be the empirical CDF. Which statement is NOT true?
- GATE 2022 ST Q15 – For iid observations with CDF F and empirical CDF F n,let D n=sup x F n(x)−F(x) and T n=√nD n. I:the law of T n is the same for all continuous F. II:D…
- GATE 2022 ST Q35 – Eight iid observations have density x/8 on 0<x<4,zero elsewhere. If α=Var[F₈(2)] for their empirical CDF,find 128α as an integer.
- GATE 2023 ST Q65 – For observations 0.13,0.12,0.78,0.51,test a Uniform(0,1) CDF against a general alternative with the two-sided Kolmogorov–Smirnov statistic D. Under…
- GATE 2024 ST Q26 – A sample of 40 has category counts (5,8,12,15) across four categories. A chi-square goodness-of-fit test checks all category probabilities equal to…
- GATE 2025 ST Q22 – For iid X n with CDF F, let F n be the empirical CDF. At a fixed real x, which holds?
- GATE 2026 ST Q23 – For an iid sample X₁,…,X n,n≥2, let Z n(x) be the proportion of observations ≤x. Which hold?