Question: An insurance coverage has an ordinary deductible of 500. Losses follow a Pareto distribution with parameters alpha= 3, theta= 1000.

Calculate the excess of the loss elimination ratio (LER) after 10% inflation over the original loss elimination ratio.

I am getting confused with the question:
When i solve the question with the E(X^d) formula from the exam C table I am getting 0.5555 for the LER for the original X

but if i am getting 0.44444 when i solve for the LER for the original X using the formula LER = 1 - [e(500) * S(500)] / 500

The book says the 2nd method is appropriate. I don't know why the first formula is not giving me the same answer as the second formula.

Please help