Question: Refertothedefinitionsofchi-squaredand T random variablesin Section 4.4.5. (a) Fromtherepresentation (Z2 1 ++Z2 d) with standardnormals,explainwhythe 2 d distribution hasmean d. (b) Fromtherepresentation T = Z~

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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