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Home work 1 Mitchell Francis Statistics 4620 1. A) min = 1               π .25 = .25(6) + .75(7) = 6.75       π .50  = .5(31) + .5(33) = 3               π .75 = .75(82) + .25(117) = 90.75      max = 527 B) IQR = Q3-Q1 = 90.75-6.75 = 84      Suspected outliers:  Q3 + 1.5(IQR) = 90.75 + 1.5(84) =  Q1 - 1.5(IQR) = 6.75 - 1.5(84) =       Outliers:  Q3 + 3(IQR) = 90.75 + 3(84) =  Q1 - 3(IQR) = 6.75 - 3(84) = 2.  A). hr(w) =  n! ( r 1 ) ! ( n r ) ! w r 1 ( 1 w ) n r         E [ wr 2 ] = 0 1 w 2 hr ( w ) dw                 E [ wr 2 ] = 0 1 w 2 n! ( r 1 ) ! ( n r ) ! w r 1 ( 1 w ) n r dw         E [ wr 2 ] = r + 1 n + 2 r n + 1 0 1 n + 2 ! ( r + 1 ) ! ( n r ) ! w r + 1 ( 1 w ) n r dw   E [ wr 2 ] = r ( r + 1 ) ( n + 2 ) ( n + 1 ) ( 1 ) E [ wr 2 ] = r ( r + 1 ) ( n + 2 ) ( n + 1 )

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3. A)  f ( x ) = e x    F ( x ) = e x =− e x      gr(y) =   n! ( r 1 ) ! ( n r ) ! [ F ( y ) ] r 1 [ 1 F ( y ) ] n r f ( y )      gr(y) =  n!
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