After applying a deductible d to a Uniform(a,b) claim with d > a, the remaining claim amount is distributed as which?

• A. Uniform(a,b-d)
• B. Uniform(0,d)
• C. Uniform(-b,-d)
• D. Uniform(0,b-d)

Answer: (D)

The key idea is the amount that remains after the deductible is the excess of the claim above d, written as R = max(0, X − d) for X ~ Uniform(a, b). If d is between a and b, some claims exceed the deductible and produce a positive remainder. Conditioning on the event X > d, X is uniform on [d, b], and subtracting d shifts this to [0, b − d]. So the nonzero remaining amount is Uniform(0, b − d). The other options either give the wrong range or include negative values, which don’t reflect the excess above the deductible.