Question

Claim amounts modelled as an exponential random variable with the mean k1000.

(a) Calculate the probability that a random variable selected claim amount is greater than k5000.

(b) Calculate the probability that a randomly selected claim amount is greater than k5000 given that it is greater than k1000

Answer 1

(a)

$$P(X>5000)=e^{-5000/1000}=e^{-5}\approx0.006738$$

(b)

$$P(X>5000|X>1000)$$

$$=P(X>4000+1000|X>1000)=P(X>4000)$$

$$=e^{-4000/1000}=e^{-4}\approx0.018316$$