document.write( "Question 1199109: Consider the random experiment of tossing two fair dice and recording the up faces. Let X be the sum of the two dice, and let Y be the absolute value of the difference of the two dice. 1.what is the probability function of Y?
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Algebra.Com's Answer #832849 by Edwin McCravy(20056)\"\" \"About 
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document.write( "There are 36 way a pair of dice can fall:\r\n" );
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document.write( "(1,1) (1,2) (1,3) (1,4) (1,5) (1,6)\r\n" );
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document.write( "(2,1) (2,2) (2,3) (2,4) (2,5) (2,6)\r\n" );
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document.write( "(3,1) (3,2) (3,3) (3,4) (3,5) (3,6) \r\n" );
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document.write( "(4,1) (4,2) (4,3) (4,4) (4,5) (4,6) \r\n" );
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document.write( "(5,1) (5,2) (5,3) (5,4) (5,5) (5,6)\r\n" );
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document.write( "(6,1) (6,2) (6,3) (6,4) (6,5) (6,6)\r\n" );
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document.write( "for x=0, the rolls with absolute difference 0 are these 6: \r\n" );
document.write( "(1,1), (2,2), (3,3), (4,4), (5,5), (6,6).  so P(0) = 6/36 = 1/6. \r\n" );
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document.write( "for x=1, the rolls with absolute difference 1 are these 10: \r\n" );
document.write( "(1,2), (2,3), (3,4), (4,5), (5,6), (2,1), (3,2), (4,3), (5,3), (6,5).  \r\n" );
document.write( "So P(1) = 10/36 = 5/18.\r\n" );
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document.write( "for x=2, the rolls with absolute difference 2 are these 8: \r\n" );
document.write( "(1,3), (2,4), (3,5), (4,6), (6,4), (5,3), (4,2), (3,1).  \r\n" );
document.write( "So P(2) = 10/36 = 5/18.\r\n" );
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document.write( "for x=3, the rolls with absolute difference 3 are these 6: \r\n" );
document.write( "(1,4), (2,5), (3,6), (4,1), (5,2), (4,1).  \r\n" );
document.write( "So P(3) = 6/36 = 1/6.\r\n" );
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document.write( "for x=4, the rolls with absolute difference 4 are these 4: \r\n" );
document.write( "(1,5), (2,6), (5,1), (6,2).  \r\n" );
document.write( "So P(4) = 4/36 = 1/9.\r\n" );
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document.write( "for x=5, the rolls with absolute difference 5 are these 2: \r\n" );
document.write( "(1,6), (1,6).  \r\n" );
document.write( "So P(5) = 2/36 = 1/18.\r\n" );
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document.write( "So the probability function of Y is \r\n" );
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document.write( "  x   P(x) \r\n" );
document.write( "  0   6/36 = 1/6 \r\n" );
document.write( "  1  10/36 = 5/18\r\n" );
document.write( "  2   8/36 = 2/9\r\n" );
document.write( "  3   6/36 = 1/6\r\n" );
document.write( "  4   4/36 = 1/9\r\n" );
document.write( "  5   2/36 = 1/18\r\n" );
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document.write( "     36/36 = 1\r\n" );
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document.write( "The cumulative distribution function is found by accumulating\r\n" );
document.write( "value plus the sum of the values before it.\r\n" );
document.write( "  x   CP(x) \r\n" );
document.write( "  0   6/36 = 1/6 \r\n" );
document.write( "  1   6/36+10/36 = 16/36 = 4/9 \r\n" );
document.write( "  2   8/36+6/36+8/36 = 22/36 = 11/18\r\n" );
document.write( "  3   6/36+8/36+6/36+6/36 = 26/39 = 2/3\r\n" );
document.write( "  4   6/36+8/36+6/36+10/36+4/36 = 34/36 = 17/18\r\n" );
document.write( "  5   6/36+8/36+6/36+10/36+4/36+2/36 = 36/36 = 1\r\n" );
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document.write( "     36/36 = 1\r\n" );
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document.write( "Edwin
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