Worked solution · Exam P
This Exam P sample reference tests Uniform Distribution. This problem translates payment conditions back to ranges of a uniform loss. The target intersection has width 100 inside a conditioning interval of width 800, giving probability 100/800=0.125 and choice B.
Independent solution
Setup
Let L be the loss and Y the amount paid after the deductible. Express the payment as a positive-part transformation.
Model
Translate both payment inequalities to loss thresholds before forming the conditional event.
Compute
Under a uniform distribution, the ratio of probabilities is the ratio of interval lengths.
Answer
The requested conditional probability is 0.125.
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.
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Original practice · fully worked
A robot arm's horizontal position X, in centimeters, has distribution function F(x)=(x/10)³ for 0<x<10. A monitor records the absolute deviation D=|X-4| from a target mark. Given that D is less than 3 centimeters, calculate the probability that D exceeds 1 centimeter.
The condition D<3 restricts X to (1,7), while D>1 retains the two pieces (1,3) and (5,7). Their total probability is 0.244 within a conditioning probability of 0.342, giving 122/171=0.71345 and choice E.
Setup
Translate the observed absolute-deviation bound into an interval for the original position.
Model
Within the conditioning interval, exceeding one centimeter of deviation produces two disjoint position ranges.
Compute
Use CDF differences for the two favorable pieces and divide by the probability of the full conditioning interval.
Answer
The conditional probability rounds to 0.713.
Keep practicing
These references share syllabus concepts or sit nearby in the official sequence. All 387 Exam P univariate random variables practice problems.
Drill the method: Exam P Conditional Probability problems · Exam P Uniform Distribution problems
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