Independent solution

How to solve this Exponential Distribution question

Setup

Setup

Translate an exact maximum payment into a tail event for the uncapped loss.

Y=min⁡(X,3000),{Y=3000}={X≥3000}Y=\min(X,3000),\qquad \{Y=3000\}=\{X\ge3000\}

Model

Model

Use the exponential survival function with mean 2000.

SX(x)=e−x/2000S_X(x)=e^{-x/2000}

Compute

Compute

Evaluate the survival probability at the policy limit.

Pr⁡(Y=3000)=e−3000/2000=e−1.5\Pr(Y=3000)=e^{-3000/2000}=e^{-1.5}
=0.2231301601…=0.2231301601\ldots

Answer

Answer

The maximum payment occurs with probability approximately 0.223.

0.223(B)\boxed{0.223\quad\text{(B)}}