Independent solution

How to solve this Uniform Distribution question

Setup

Setup

Let X denote the loss and express a positive payment threshold as a threshold on X.

X∼Uniform⁡(0,2)X\sim\operatorname{Uniform}(0,2)
Y=(X−d)+Y=(X-d)_+

Model

Model

Use the supplied payment tail to recover the deductible.

0.30=Pr⁡(Y≥1.20)=Pr⁡(X≥d+1.20)0.30=\Pr(Y\ge1.20)=\Pr(X\ge d+1.20)
0.30=2−(d+1.20)20.30=\frac{2-(d+1.20)}{2}

Compute

Compute

Solve for the deductible and evaluate the new uniform tail.

d=0.20d=0.20
Pr⁡(Y≥1.44)=Pr⁡(X≥1.64)=2−1.642=0.18\Pr(Y\ge1.44)=\Pr(X\ge1.64)=\frac{2-1.64}{2}=0.18

Answer

Answer

The second payment threshold is reached with probability 0.18.

0.18(C)\boxed{0.18\quad\text{(C)}}