It would be helpful if you stated your pareto distribution.
I only deal with one parameter (p) with the pareto.
I would guess that theta is a shift.
I start the density at 1, but you may be starting it at theta.
the block of car insurance business you are considering, there's 50% chance that a claim will be made during upcoming yr. once a claim is submitted, the claim size has the pareto distribution with parameters 3 and 1000 (theta) . only one claim will happen during the yr. determine the variance of the unconditional distribution of the claim size.
in the solution, it says let x be the random claim size. the prob. distribution is mixed distribution : 50% in the pareto distribution and 50% in a point-mass at 0.
I don't understand where does the 50% come. And i only know the pdf , E(x) for pareto function and have no idea about what pareto distribution is. Help appreciated!