Question

The loss due to an earthquake in a commercial building is modelled by a random
variable X with density function
f(x) =  0:005(20 0; − x); for 0 elsewhere < x < 20
Given that the fire loss exceeds 10, what is the probability that it exceeds 18.

Answer 1

P(X>x)=∫ ²⁰_x0.005(20-x)dx=0.0025(20-x)²,0<x<20

P(x>18|x>10)=P(x>18)/P(x>10)=(20-18)²/(20-10)²=0.04