Question

A4. 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 < x < 20
0, elsewhere
Given that the fire loss exceeds 10, what is the probability that it exceeds 18

Answer 1

P(X>x)=$\intop$²⁰_x0.005(20-t)dt=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