Dear Mentor,
Could you please guide me the following issue?
The value of CDF between the interval 0<= x < 1 should be according to the area of PDF from the interval x=0 to x, that is (x-0)(1).
May i know why the value of it as shown in the lecture is (x-0)/1 ?
Thank you.
Were you able to find an answer to your question?
Dear Mr Tom Mosher,
I think that the area of rectangle should be width X height, that is (x-0)(1).
It is not (x-0)/1 as shown in the lecture.
Thank you.
It comes from this image on the previous slide:
He’s just invented an equation that linearly interpolates between 0 and 1 as x moves from a to b.
If x = a, then the equation simplifies to 0 / (b-a) = 0
If x = b, then the equation simplifies to (b-a) / (b-a) = 1.
Actually, I struggled a bit with this notion too so if some people are still struggling, here’s how I see it :
_the total area of the PDF ( orange area on the left graph ) is 1
_the Y axis on the CDF ( the “Fx” axis ) corresponds to the “cumulated” PDF area for a given x, you can see that this axis goes from 0 to 1 as well
_the (x-0)/1 formula is referring to this ratio: (PDF area from 0 to x) / (total PDF area)
=> PDF area from 0 to x = (x-0)(1) same as (x - 0) in the picture
=> Total PDF area = 1
=> therefore (x-0)/1 corresponds to the “portion” of the PDF area up to x
I hope this helps !
Pierre
