Refertothedefinitionsofchi-squaredand T random variablesin Section 4.4.5. (a) Fromtherepresentation (Z2 1 ++Z2 d) with standardnormals,explainwhythe 2 d distribution
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Refertothedefinitionsofchi-squaredand T random variablesin Section 4.4.5.
(a) Fromtherepresentation (Z2 1 +⋯+Z2
d) with standardnormals,explainwhythe χ2 d distribution hasmean d.
(b) Fromtherepresentation T = Z~
»
X2~d, explainwhythe t distribution convergestothe standard normalas d → ∞. (Hint: Applytheweaklawoflargenumbersinsidethesquare root,andthenapplySlutzky’sTheorem,statedinthepreviousexercise.)
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Foundations Of Statistics For Data Scientists With R And Python
ISBN: 9780367748456
1st Edition
Authors: Alan Agresti
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