One observation has density 2x/θ² on 0<x<θ. Using pivot X/θ,which interval is an 80% confidence interval for θ when x=10? Limits are rounded to three decimals.
The pivot U=X/θ has CDF u² on (0,1). Its .1 and .9 quantiles are √.1 and √.9. Thus P(√.1<U<√.9)=.8. Inverting gives (x/√.9,x/√.1)=(10.541,31.623). **A**.
More Confidence Intervals questions
GATE 2021 ST Q14– A realization of n≥2 iid N(μ,σ²) observations is given,μ∈ℝ,σ>0. P:a 95% confidence…
GATE 2026 ST Q33– A sample of size 10 has density 2(x−μ)e(−(x−μ)²) for x>μ, zero otherwise. Its observed…
GATE 2022 ST Q18– An iid sample of size 18 has density 2x exp(−x²/θ)/θ on x>0,zero otherwise. Let T=Σx…