document.write( "Question 1160790: A mathematics professor gives an \"extra-credit\" (bonus marks) problem on a test. If it is done correctly,15 points are added to the test score, and if it is done partially correctly,5 points are added; otherwise 5 points are subtracted. Suppose a student's probability of getting the problem completely right is 1/4, and only partially correct is 1/2.\r
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Algebra.Com's Answer #852214 by ikleyn(52781) $\"\"$ $\"About$

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\n" ); document.write( "A mathematics professor gives an \"extra-credit\" (bonus marks) problem on a test.
\n" ); document.write( "If it is done correctly, 15 points are added to the test score,
\n" ); document.write( "and if it is done partially correctly, 5 points are added;
\n" ); document.write( "otherwise 5 points are subtracted.
\n" ); document.write( "Suppose a student's probability of getting the problem completely right is 1/4, and only partially correct is 1/2.
\n" ); document.write( "Find the student's mathematical expectation 𝐸 (expected value) for extra credit.
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document.write( "This problem is easy.\r\n" );
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document.write( "Make a table, placing scores for extra credit in the upper row (3 possible values)\r\n" );
document.write( "and placing corresponding probabilities for these scores in the lower row, according to the problem.\r\n" );
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document.write( "Extra score, x       15     5      -5\r\n" );
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document.write( "Probability, p       1/4    1/2    1/4\r\n" );
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document.write( "Notice that the last value in the lower row is  1/4 = 1 - 1/2 - 1/4 ,\r\n" );
document.write( "complementing the sum of two other values in this row to 1.\r\n" );
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document.write( "Now form the sum  for the expectation\r\n" );
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document.write( "    E =  +  +  =  =  =  = 5.\r\n" );
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document.write( "ANSWER.  The expected value for extra credit is 5.\r\n" );
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