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Solutio n: () 3 931 31 3! 4! 5! 6! 3 121 221 321 421 21 1! 2! 2! 2! 3! 2! 4! 2! 7! 8! 9! 10! 11! 521 621 721 821 921 5! 2! 6! 2! 7! 2! 8! 2! 9! 2! 9! 7! 2! #1 Method CC C C C C C C C CCC Ans ×××× ××××× × Δ= + + + + + +++++ = Δ 9 2 12 3 #2 9! 36 9 = 12! 220 55 9! 3! Method C Ans C ⎛⎞ ⎜⎟ × ⎝⎠ == = × . Solutio Let X = The final grade 15 68 12 72 82 = X X = 80.5 Solutio Reference #1

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Reference #2
() ( ) ( ) ( ) ( ) ( ) ( ) m X P n X P m n P m X P n X P m X m n X P n X P m X P m X m n X P > > = + > > = > + > > = > > + > ( ) ( ) ( ) ( ) ( ) ( ) p p n X P p p p p X P X P X P p p p p X P X P X P p X P let n 1 2 3 2 2 1 1 1 ) 1 ( 3 2 3 1 1 1 2 1 2 1 = = = = > > = = = = > > = = = = # Thus X is a geometric random variable. Solutio n: Solutio 8 2 468 222 C Ans CCC = ++

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Solutio n: () = P(X is a man | X is playing piano) P(X is a man and playing piano) = P(X is playing piano) 0.6 0.3 = 0.6 0.3 0.4 0.7 0.18 9 = 0.3913 39% 0.46 23 Ans × = ×+× == Solutio P(X = n) = ,... 3 , 2 , 1 , ) 10 9 )( 10 1 ( 1 = n n E(X) = = 1 1 ) 10 9 )( 10 1 ( * i i i Thus, E(X) = 2 ) 10 9 1 ( 1 * 10 1 = 10 E(X 2 ) = = 1 1 2 ) 10 9 )( 10 1 ( * i i i E(X 2 ) = 2 ) 10 9 1 ( 10 9 1 * 10 1 + = 190
Var(X) = E(X 2 ) – [E(X)] 2 = 190 - 10 2 = 90 P(Y = m) = P(X = 2 1 m ) = ,... 7 , 5 , 3 , ) 10 9 )( 10 1 ( 2 3 = m m

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