an insurance company has sold a policy to a customer, who could incur in a loss X(w) with probability density:
f(x)= 10^-6 x e^(-x/1000) for x>0
= 0 elsewhere
1)assume that the probability of arrival of the loss is 2%. using such info compute the expected value of the loss.
") the policy covering this risk is of the type stop-loss: in the case the claim exceeds 3000$ this is the amount paid by the insurer. Taking into account also that the claim addressed to the insurer, in the case of loss, is of amount Y(w)=0.9X(w) compute the expected claim.
how do I do these? I can't figure out the reasoning. thanks in advance for your great help.
is the probability that the loss is x, given that there is some loss.
0.02 is the probability that there is some loss.
Hence the probabability of loss x is p(x)=0.02 f(x).
Therefore the expected loss is:
integral(x=0, infty) x (0.02 f(x)) dx