Question

An insurance policy pays for a random loss X subject to a deductible of 550. The loss amount is modeled as a continuous random variable with density function 4500 for x > 500 f(x) = { otherwise Determine the expected payment made under this insurance policy.

Answer 1

here expected payment after deductible= E(X-550)=$\int_{550}^{\infty }$ (4/500)*(x-550)*(500/x)⁵ dx

=-(4/500)*(500⁵/3x³ -550*500⁵/4x⁴) |^$\infty$₅₅₀ =125.2191 ~ 125