For a marine hull insurance policy, a claim occurs with probability 0.DD, where DD represents the two date-digits of your birthday (DD.MM.YYYY). If a claim occurs, it has a probability density given by

fB(x)=c·x^(−1.5), 1<x<YYYY,

where YYYY are the four digits of your birth year and c is a constant to be determined. Determine the c.d.f. and the first two moments of both B (the claim given it occurs) and X (the payment to the policy). Plot the two c.d.f.’s.

I set that the integral of my pdf from 1 to YYYY has to be equal to 1, so I found c.

But the problem is that when I integrate the pdf in order to find the cdf, I have a negative cdf, which cannot be. How do you deal with negative power in a pdf ?