document.write( "Question 999826: x 1 2 3 4 5
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Algebra.Com's Answer #617385 by AnlytcPhil(1807)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "1. Let X represent the number of times your professor goes to the gym \r\n" );
document.write( "each week.  You are given the following probability table for X. \r\n" );
document.write( "Unfortunately, your professor spilled some coffee on the probability \r\n" );
document.write( "for x = 5 and it is now illegible.\r\n" );
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document.write( "x          1      2      3      4     5\r\n" );
document.write( "P(X = x) 0.12   0.25   0.38   0.17   ???\r\n" );
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document.write( "(a)	What is P(X = 5)?\r\n" );
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document.write( "All the probabilities must add up to 1, the probability of certainty,\r\n" );
document.write( "because it is certain that one of them will occur.\r\n" );
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document.write( "So add 0.12 + 0.25 + 0.38 + 0.17 and get 0.92\r\n" );
document.write( "Then subtract 1.00 - 0.92, and get 0.08\r\n" );
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document.write( "So now we know that what he spilled coffee on was 0.08\r\n" );
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document.write( "x          1      2      3      4     5\r\n" );
document.write( "P(X = x) 0.12   0.25   0.38   0.17  0.08 \r\n" );
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document.write( "(b)	Find the expected value of X.\r\n" );
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document.write( "Multiply each x by the corresponding probability P(X=x) and add:\r\n" );
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document.write( "E(X) = 1×0.12 + 2×0.25 + 3×0.38 + 4×0.17 + 5×0.08 = 2.84 \r\n" );
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document.write( "(c)	Find the standard deviation of X.\r\n" );
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document.write( "\"sigma=sqrt%28E%28X%5E2%29%5E%22%22-%28E%28X%29%5E%22%22%29%5E2%29\"\r\n" );
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document.write( "E(X) = 2.84\r\n" );
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document.write( "E(X²) = 1²×0.12 + 2²×0.25 + 3²×0.38 + 4²×0.17 + 5²×0.08 = 9.26\r\n" );
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document.write( "\"sigma=sqrt%289.26-%282.84%29%5E2%29\"\r\n" );
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document.write( "\"sigma=1.092886087\"\r\n" );
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document.write( "Edwin
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