SOLUTION: 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 correctl
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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.
Find the student's mathematical expectation 𝐸 (expected value) for extra credit. Answer by ikleyn(52781) (Show Source):
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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.
Find the student's mathematical expectation 𝐸 (expected value) for extra credit.
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This problem is easy.
Make a table, placing scores for extra credit in the upper row (3 possible values)
and placing corresponding probabilities for these scores in the lower row, according to the problem.
Extra score, x 15 5 -5
Probability, p 1/4 1/2 1/4
Notice that the last value in the lower row is 1/4 = 1 - 1/2 - 1/4 ,
complementing the sum of two other values in this row to 1.
Now form the sum for the expectation
E = + + = = = = 5.
ANSWER. The expected value for extra credit is 5.
