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# S2.... Pdf/cdf watch

1. i dont understand the difference between a pdf and a cdf! i know how to switch from one to the other etc but i dont understand what the actual difference between them is! can anyone help? xx
2. A cdf is a function which defines the probability that a random variable X is less than or equal to some value x whereas a pdf will give the probability that the random variable is exactly equal to some value x. Furthermore, continuous random variables are normally defined by a cdf.

To give an example.....a fair 6 sided dice is rolled and the random variable X is the number obtained on rolling the dice...

the pdf....

P(X=x) = 1/6 (and x can be any of 1,2,3,4,5,6)

the cdf....

P(X less than or equal to x) = x/6 (again where x can be any of 1,2,....,6)

Hope this helps
3. The cdf has an obvious meaning its the probability that a randomly generated outcome will be lower than a given value.
Eg if a distribuion is uniform on 0,2 the cdf of 1 is 1/2

The pdf. is less obvious, the best way to think about it is with an analagy of a steel rod.

At a given point on a rod (x) there is no mass as x has no "width" however we can think about the dencity at a point.

The pdf at x is the dencity at x and the cdf at x is the mass of the rod less than x.

Hope that helps
4. Thanx guys.... its clearer now. i jus don't wanna chance not completely understanding something that might come up on the exam. xx
5. oww, im stuck again! if with a pdf we can only look at P(X=x) and with a cdf we can look at P(X ≤ x), why is it that in my revision guide it says that using a pdf, P(c ≤ x ≤ d)= ∫ (between c and d) of f(x)dx
6. althoguh it has no values a point the intergral still exist.
The intergral over an interval of a graph gives you the area but the area at any given point is 0

the area of a square at any given line is 0 but between 2 lines the area exists

Similarly with probability the probabilty of a certain value is 0 with a continous distribution but between 2 values the probability exists.

This is why the integral of the pdf is the cdf

Rember the pdf does not give you the probabilty of x at x
With a continuos distribution P(X=x) = 0 for all x
7. I get it now! its because by integrating f(x) u get F(x) and this is the cdf!
8. Sorry to bring back this thread, but really confusing. How do you know when to integrate/differentiate?
And when do you know which one ( pdf or cdf) to use when finding out P(X>value)? Confused!
9. (Original post by theseeker)
Sorry to bring back this thread, but really confusing. How do you know when to integrate/differentiate?
And when do you know which one ( pdf or cdf) to use when finding out P(X>value)? Confused!
They should tell you e.g p.d.f given by random variable X so P(X>value) would be calculated from the pdf.
10. (Original post by MoMatrix)
They should tell you e.g p.d.f given by random variable X so P(X>value) would be calculated from the pdf.
It's CDF.

I really don't know, when to know to use pdf or cdf? I know when they're asking for specific, you use, PDF..etc but like mode..etc because im getting the wrong answers at the moment.

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Updated: April 30, 2011
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