Worked solution · Exam P
This Exam P sample reference tests Binomial Distribution. The number of covered occurrences is binomial with five trials and probability 0.5. Capping the count at three gives an expected payment of 30(73/32) = 68.4375, so the nearest listed value is D.
Independent solution
Setup
Let N count the covered occurrences across the five independent periods.
Model
Group all counts of three or more at the contractual payment limit.
Compute
Use the symmetric binomial probabilities with denominator 32.
Answer
The expected payment rounds to the listed value 68.
Test the method on unseen problems
30 original univariate random variables problems with complete solutions and wrong-choice analysis. Written for Exam P, not copied from the SOA set. One-time $19 PDF.
Error diagnosis
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Original practice · fully worked
A fabrication line completes seven independent production runs. Its safety relay is triggered on any run with probability 0.25. A reliability rebate ignores the first two triggers, then pays 50 for each additional trigger, subject to at most three paid triggers. Calculate the expected rebate.
For a binomial trigger count N, the number of paid triggers is min((N-2)+,3). Its expectation is the sum of the three binomial tails beginning at 3, 4, and 5, which equals 0.3270263672. Multiplication by 50 gives 16.35131836, so choice C is correct.
Setup
Let N count relay triggers over the seven independent runs and translate the two-trigger threshold and three-payment ceiling into a payment variable.
Model
Apply the tail-sum identity to the paid-trigger count, whose possible values are zero through three.
Compute
Evaluate the three required binomial tails and multiply their sum by the rebate per paid trigger.
Answer
The expected reliability rebate rounds to 16.351.
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