CDF of a PDF with a negative power

I need to solve the following problem:

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 ?


Well-Known Member
Did you put in the limits of integration from 1 to 2000 or whatever? It will come out positive because it is all above the x axis.


Super Moderator
It would seem to me that you might want to consider integrating the function (i.e. solving for the constant ("c") from 1 to Infinity; which gives the result for "c" that will provide the pdf and cdf. In terms of moments, you have to specify a finite upper limit (e.g. 2000 as suggested above) because the integral will (theoretically) fail to converge to infinity.