# What exactly is the difference bet. a CDF and a PDF?

Peon666

## Homework Statement

I understand that PDF is a derivative of CDF and hence CDF is the integral of PDF. But I don't understand the difference between PDF and simply probability? What exactly is the differece? What extra things does PDF tell us which simple probability does not?

## Homework Equations

For example, we toss a coin and a head comes. Probability of it is 1/2. What's PDF in this case?

## The Attempt at a Solution

Homework Helper
Well say you toss a coin 1000 times and you want the probability of exactly 3 heads. To write down all the possibilities, would take a long time. The pdf is basically a single formula that would describe the probabilities. So for the coin toss (it follows a binomial distribution)
P(X=3)= 1000C3(1/2)3(1/2)1000-3

A cdf sums the probabilities.

EDIT: that is for a discrete distribution

Last edited:
Peon666
I think I'm getting to the idea but I'm not completely clear yet. I understand the difference between CDF and PDF but what's the difference between simple probability and PDF?

And do we always follow the binomial distribution in PDF?