Aprobabilitydistributionhasa scaleparameter if, whenyoumultiply byaconstant c, all valuesinthedistributionmultiplyby c Ithasa locationparameter if, whenyouincrease byaconstant c, allvaluesinthedistributionincreaseby c (a) Forascaleparameter , thedistributionof Y doesnotdependon Showthatforthe gamma distribution(2 10)with 1 , Y has meanandvariancenotdependenton (b) Foralocationparameter , the pdf is afunctionof y and thedistributionof Y doesnotdependon Foranormaldistribution,showthat is alocationparameter

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Question: Aprobabilitydistributionhasa scaleparameter if, whenyoumultiply byaconstant c, all valuesinthedistributionmultiplyby c. Ithasa locationparameter if, whenyouincrease byaconstant c, allvaluesinthedistributionincreaseby c. (a) Forascaleparameter , thedistributionof

Aprobabilitydistributionhasa scaleparameter θ if, whenyoumultiply θ byaconstant

c, all valuesinthedistributionmultiplyby

c. Ithasa locationparameter θ if, whenyouincrease θ

byaconstant

c, allvaluesinthedistributionincreaseby c.

(a) Forascaleparameter θ, thedistributionof Y ~θ doesnotdependon θ. Showthatforthe gamma distribution(2.10)with θ = 1~λ, Y ~θ has meanandvariancenotdependenton θ.

(b) Foralocationparameter θ, the pdf is afunctionof y − θ and thedistributionof Y − θ

doesnotdependon θ. Foranormaldistribution,showthat μ is alocationparameter.

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