Worked solution · Exam P
This Exam P sample reference tests Expected Value. The five possible payments are 100, 200, 300, 350, and 400. Weighting them by probabilities 5/15 through 1/15 gives 220, choice C.
Independent solution
Setup
List the payment associated with each of the five possible outcomes. The outcome probabilities are proportional to five, four, three, two, and one.
Model
The expected payment is the probability-weighted sum of the five payment amounts.
Compute
The weighted numerator is 3,300 and the probability denominator is 15, giving expected payment 220.
Answer
The expected payment is 220, selecting choice C.
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Original practice · fully worked
A short-stay plan reimburses 80 per night for the first two nights and 40 for the third night. Stay length N has probabilities 0.10, 0.30, 0.40, and 0.20 for zero, one, two, and three nights. Find the variance of the reimbursement.
The payment mean is 128 and its second moment is 20,160. Subtracting 128² gives variance 3,776, choice D.
Setup
The reimbursement takes values zero, 80, 160, and 200 according to the stay length. Weighting these values gives mean 128.
Model
Compute the second raw moment by weighting the squared reimbursement values by the same stay probabilities.
Compute
Subtract the squared mean from the second raw moment. The resulting variance is 3,776.
Answer
The reimbursement variance is 3,776, selecting choice D.
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