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.
f(x)=10^-6 x e^(-x/1000)
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
RonL