Question: Forabinomialsample proportion , showthattheapproximatevarianceof sin1( ) (with the anglebeingmeasured in radians)is1/4n, sothisisavariancestabilizingtransformation. (In reality,simulationrevealsthatthevarianceofthis arcsinetransformation is notnearly constantwhen is near0ornear1and n is notverylarge.)

Forabinomialsample proportion ˆπ, showthattheapproximatevarianceof sin−1(

º

ˆπ) (with the anglebeingmeasured in radians)is1/4n, sothisisavariancestabilizingtransformation.

(In reality,simulationrevealsthatthevarianceofthis arcsinetransformation is notnearly constantwhen π is near0ornear1and n is notverylarge.)

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