This is the ordered-sample density for three iid variables with base density g(x)=3x²/2 on[−1,1], since3!×(3/2)³=81/4. Ordering does not alter their sum. The base variable has mean0 and second moment(3/2)∫₋₁¹x⁴dx=3/5. Independence before ordering gives sum variance3×3/5=1.8.
More Order Statistics questions
GATE 2025 ST Q44– Independent X,Y₁,Y₂ have exponential rates 2,1,1 respectively. R i is the ascending rank…
GATE 2024 ST Q32– Three iid observations have density 2x on (0,1),zero otherwise. Find P(min(X₁,X₂,X₃)≥E X₁)…
GATE 2022 ST Q53– Three iid observations have density 2x on (0,1),zero elsewhere. Let p be the probability…
GATE 2022 ST Q62– Y₁<⋯<Y n are order statistics of an iid sample from a continuous distribution symmetric…
GATE 2021 ST Q27– The kth order statistic from a size-eight Uniform(0,2) sample has density (7/32)x⁶(2−x)…
GATE 2021 ST Q48– X (1)<⋯<X (5) are order statistics of a size-five Uniform(0,θ) sample. P:3X (2) is…