Var(¯X/s) = (n-1)/(n(n-3)) | t-Distribution Variance | IIT JAM MS 2025 | Problem - 28 | RitwikMath
Автор: RitwikMath
Загружено: 2025-12-02
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This IIT JAM Mathematical Statistics 2025 PYQ asks for the variance of the sample mean divided by sample standard deviation: Var(¯X/s) where X₁,…,Xₙ ~ N(0,1). The solution recognizes that √n · (¯X/s) ~ t_{n-1}, so ¯X/s = t/√n, and thus Var(¯X/s) = Var(t)/n.[web:48][web:49]
For a t-distribution with ν = n-1 2 degrees of freedom, Var(t) = ν/(ν-2) = (n-1)/(n-3), giving Var(¯X/s) = [(n-1)/(n-3)] / n = (n-1)/(n(n-3)). This leverages the independence of ¯X and s, a key property of normal samples.[web:48][web:53]
Essential for mastering t-distribution moments and their applications in IIT JAM MS, GATE ST, and other statistics entrance exams.
#IITJAMMS #IITJAMMS2025 #IITJAMMathematicalStatistics #tDistribution #StudentstDistribution #SampleMean #SampleVariance #DegreesOfFreedom #NormalDistribution #GATESTatistics #GATE2025 #StatisticsPYQ #CSIRNETStatistics #UPSCStatistics #PointEstimation
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