Question

A company offers earthquake insurance. Annual premiums are modeled by an exponential random variable with mean 2. Annual claims are modeled by an exponential random variable with mean 1. Premiums and claims are independent. Let X denote the ratio of claims to premiums. What is the density function of A?

Answer 1

The density function of X is :
`h_(X) (x) = \left \{ {{(2)/((1+2x)^(2) ) \quad x\geq0} \atop {x=0 \qquad x<0 }} \right.`

Explanation:

`h_(X) (x) = \left \{ {{(2)/((1+2x)^(2) ) \quad x\geq0} \atop {x=0 \qquad x<0 }} \right.`

For easiness and clarity of expression, the calculations are handwritten and attached as files. The files are broken into bits for easy understanding. Check the six files below for the calculations.