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1. Let's break this down more.

1) You have a PDF, call it f(x), it is (2.5(200^2.5))/x^3.5 defined on range [200, infinity)

2) To calculate your CDF, call it F(x), you would take the integral of your pdf between 200 and <some variable>, in this case you have it set up as F(x) = integral( (2.5(200^2.5))/t^3.5 dt from 200 to x]

You should know that F'(x) = f(x), figuring out f'(x) is useful for other things (such as hazard/survival function but not for anything you're doing here so if that's what you're calculating... I have to ask why?).

So let's do the integral that we have in 2), this is a simple power rule so you get 2.5*200^{2.5}/(-3.5+1) *t^{-2.5} from 200 to x which is basically the same as -200^{2.5}/t^{2.5} from 200 to x, so now plug in your limits to get:

-200^{2.5}/x^{2.5} - (-200^{2.5}/200^{2.5}) = -200^{2.5}/x^{2.5} + 1 or if you want to re-write it 1 - 200^{2.5}/x^{2.5} which is your CDF.

If you want, you can differentiate THAT to get your f(x) or 2.5*200^{2.5} / x^{3.5}  Reply With Quote

2. Originally Posted by NoMoreExams What function are you taking the derivative of? Is your function

1) (2.5(200^2.5))/t^3.5

2) Integral[ (2.5(200^2.5))/t^3.5 dt from 200 to x ]

Those are 2 different functions.
The first one.  Reply With Quote

3. Originally Posted by aomara The first one.
See my other post. What are you hoping to accomplish by taking the derivative of a pdf?  Reply With Quote

4. Originally Posted by NoMoreExams Let's break this down more.

1) You have a PDF, call it f(x), it is (2.5(200^2.5))/x^3.5 defined on range [200, infinity)

2) To calculate your CDF, call it F(x), you would take the integral of your pdf between 200 and <some variable>, in this case you have it set up as F(x) = integral( (2.5(200^2.5))/t^3.5 dt from 200 to x]

You should know that F'(x) = f(x), figuring out f'(x) is useful for other things (such as hazard/survival function but not for anything you're doing here so if that's what you're calculating... I have to ask why?).

So let's do the integral that we have in 2), this is a simple power rule so you get 2.5*200^{2.5}/(-3.5+1) *t^{-2.5} from 200 to x which is basically the same as -200^{2.5}/t^{2.5} from 200 to x, so now plug in your limits to get:

-200^{2.5}/x^{2.5} - (-200^{2.5}/200^{2.5}) = -200^{2.5}/x^{2.5} + 1 or if you want to re-write it 1 - 200^{2.5}/x^{2.5} which is your CDF.

If you want, you can differentiate THAT to get your f(x) or 2.5*200^{2.5} / x^{3.5}
Ok I see what I was doing wrong. Thank you very much.  Reply With Quote