A Simple Question About the Cumulative Density Function

[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}

[aomara]

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.

[NoMoreExams]

The first one.

See my other post. What are you hoping to accomplish by taking the derivative of a pdf?

[aomara]

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.