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−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)=∫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