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55010Solution5

# 55010Solution5 - STAT 550 Homework 5 Solution 2.4-2(a y 2 1...

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1 STAT 550 Homework 5 Solution 2.4-2 (a) 2 1 ( ) 0.2 0.34 y p y 2 2 2 2 2 2 2 ( ) ( ) ( 2)(0.20) ( 1)(0.34) 0 0.15 2(0.1) 3(0.05) 0.24 ( ) ( ) ( ) ( 2 0.24) (0.2) ( 1 0.24) (0.34) (0 0.24) (0.16) (1 0.24) (0.15) (2 0.24) (0.10) (3 0.24) (0.05) 2.0824 Y Y Y E Y yp y Var Y Y E p y             (b) 2 2 2 2 2 ( ) ( ) [ ( )] ( ) ( 0.24) 4 0.2 1 0.34 0 1 0.15 4 0.1 9 0.05 0.24 2.0824 Y Var Y E Y E Y y p y       (c) 2 (2 3 ) ( 3) ( ) 9 2.0824 18.7416 Var Y Var Y   2.4-3 (a) 2 2 2 2 ( ) ( ) (0)(0.25) (1)(0.25) 2(0.20) 3(0.10) 4(0.10) 5(0.10) 1.85 ( ) 0 (1)(0.25) 4(0.20) 9(0.10) 16(0.10) 25(0.10) 6.05 ( ) ( ) [ ( )] 6.05 1.85 2.6275 ( ) ( ) 1.62 X E X xp x E X Var X E X E X STD X Var X (b) 2 2 100 350 ( ) 100 350 ( ) 747.5 ( ) ( ) (100 350 ) 350 ( ) 350 2.6275 567.33 Let y x E y E x STD y Var y Var x Var x 2.6-1

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2 1 2 2 2 2 2 2 2 2 2 2 2 2 1 1 (11 9 3 7 8 1 5 12 3 10) 6.9 10 1 ( ) 1 [(11 6.9) (9 6.9) (3 6.9) (7 6.9) (8 6.9) (1 6.9) 10 (5 6.9) (12 6.9) (3 6.9) (3 6.9) (10 6.9) ] 3.56 n i i X Xi n S X X n 2.6-2 1 2 3 5 4 6 ( ) 15 15 15 x p x 1 1 1 (1 5 2 4 3 6) 2.07 15 n i X Xi n
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