CDF and PDF functions?!

[shellbyville]

So I'm reading in my calculus book right now about cumulative distribution functions and probability density functions and I am just completely lost. I've read the chapter twice and I still have no idea what they are or how to change graphs from one to the other. Can someone help me out and explain this to me in dummy-speak?

Thanks so much!
xoxo

 

[Deleted member 4993]

So I'm reading in my calculus book right now about cumulative distribution functions and probability density functions and I am just completely lost. I've read the chapter twice and I still have no idea what they are or how to change graphs from one to the other. Can someone help me out and explain this to me in dummy-speak?

Thanks so much!
xoxo

Did you read:

http://en.wikipedia.org/wiki/Cumulative_distribution_functions

and

http://en.wikipedia.org/wiki/Probability_density_function

 

[shellbyville]

Did you read:

http://en.wikipedia.org/wiki/Cumulative_distribution_functions

and

http://en.wikipedia.org/wiki/Probability_density_function

Yes I did. It's quotes like this: "describes the probability that a real-valued random variable X with a given probability distribution will be found at a value less than or equal to x". that just leave me sitting in front of the computer like O_O.

 

[shellbyville]

---

Yes I did. It's phrases like, "In probability theory and statistics, the cumulative distribution function (CDF), or just distribution function, describes the probability that a real-valued random variable X with a given probability distribution will be found at a value less than or equal to x."that I'm not quite connecting to my brain.

 

[DrPhil]

So I'm reading in my calculus book right now about cumulative distribution functions and probability density functions and I am just completely lost. I've read the chapter twice and I still have no idea what they are or how to change graphs from one to the other. Can someone help me out and explain this to me in dummy-speak?

Thanks so much!
xoxo

When sombody says "probability distribution function," the first example I think of is the familiar bell curve of the normal distribution. But a PDF can be any function at all. so long as an integral exists so that the area can be normalized to unity. For instance, if your PDF is a series of discrete values, you normalize by dividing by the sum.

The "cumulative distribution function" is the running integral of the PDF. Its properties are that is is always increasing (since the PDF is always positive), and it increases from 0 to 1 (since the PDF is normalized to unit area). For a continuous distribution, you can think of the CDF as being the shaded area below a given point. For a discrete PDF, the CDF will be a series of upward steps.

For the continuous case, the two functions are related by

\(\displaystyle \displaystyle CDF(x) = \int_{-\infty}^x PDF(t)\ \mathrm dt \)

\(\displaystyle \displaystyle PDF(x) = \dfrac{\mathrm d}{\mathrm dx}\left( CDF(x)\right )\)