The question is as following
i) Individual claims from a block of general insurance policies are given by Y where Y = X^r & X
follows LogNormal(μ,σ2) distribution.
Show that the probability that value of an individual claim lies between A & B (B > A) is
exp(rμ + r2σ2/2)[φ(Br ) - φ(Ar )], where Xr = (log X – μ) / σ - rσ, for X = A , B.
φ(z) is the distribution function of the standard normal distribution.
My query is that the question is asking to prove the expression of probability of P(A < Y < B) as exp(rμ + r2σ2/2)[φ(Br ) - φ(Ar )], where Xr = (log X – μ) / σ - rσ, for X = A , B.
But this is the expression for E[ Y ] given A<Y<B. This doesn't seem to be a probability value to me because it will give a value exp(rμ + r2σ2/2) which is greater than 1 if we consider A =0 and B = infinity .
Please correct me if i am wrong.
Last edited by a moderator: Sep 3, 2016
