This Exam P sample reference tests Expected Value. Splitting the expectation integral at zero handles the absolute value correctly and gives 28/15, choice D.
The expectation is the integral of the value multiplied by its density. Because the density contains an absolute value, its algebraic form changes at zero.
E[X]=∫−24x10∣x∣dx
Model
Model
On the negative interval the integrand is negative, while on the positive interval it is positive. Split the integral at zero before evaluating.
E[X]=101(−∫−20x2dx+∫04x2dx)
Compute
Compute
The two contributions combine to an expected value of approximately 1.8667.
E[X]=101(−38+364)=1528
Answer
Answer
The expected value is approximately 1.8667, selecting choice D.
1528(D)
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