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# 9.15 - P A P B = 1 4 × 1 2 = 1 8 This means A and B are...

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Math 543 Probability Homework Y u Hu Homework due 9/15 1.5: 2,7 1.8: 27 1.5:2 Solution: When j < m , it is very to check that A ij ( i < j ) and A mn ( m < n ) are independent. And when j = m, P ( A ij A mn ) = P ( A ij A j n ) = { jth and nth show the same as ith } = ( 1 6 ) 2 = P ( P ( A ij ) P ( A mn )). So that they are pairwise independent. And if i = j = k , P ( A ij A j n A in ) = 1 36 = P ( A ij ) P ( A j n ) P ( A in ) = 1 216 Hence they are not independent. 1.5:7 Solution: (a). Suppose that M= { Male } , F= { Female } . Then we have A= { MMM,FFF } ; B= { MFF,FFF,FMF,FFM } ; C= { FMF,FMM,MFF,FFM,MFM,MMF } . So that A B = { FFF } ; B C = { FFM,FMF,MFF } ; A C =Φ. Hence 1 8 = P ( A B ) = P ( A ) P
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Unformatted text preview: P ( A ) P ( B ) = 1 4 × 1 2 = 1 8 . This means A and B are independent. 3 8 = P ( B ∩ C ) = P ( B ) P ( C ) = 1 2 × 3 4 = 3 8 . This means B and C are independent. (b). Since 0 = P ( A ∩ C ) 6 = p ( A ) P ( C ) = 1 4 × 3 4 . This means A and C are not independent. (c). No (d). No 1.8: 27 Solution: I am sorry! I really do not know the meaning of this problem! It is really a controversy! Please give me some hint! Thanks! 1...
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