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Let X1:3<=X2:3<=X3:3 be the order statistics from independent and identically distributed random variables X1,X2 and X3. We use the regression relation E[(X2:3-X1:3)2X2:3=x]=E[(X3:3-X2:3)2X2:3=x] to characterize the Student's t3 distribution on three degrees of freedom.
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