# Cdf and pdf

1. Feb 21, 2013

### freedominator

how are cdf and pdf related in statistics?
plz help i have a test tomorrow

2. Feb 21, 2013

### freedominator

ok i think i got it
cumulative distribution function is the integral from 0 to k of a probability distribution function of k
thats why the p(k) =F(k)-F(k-1)

3. Feb 21, 2013

### Bachelier

CDF is the probability accumulated up to the said-point k for instance (from -∞) in other words it is the area under the curve.
PDF is the probability at that point. $P(X=k)$ meaning it is the height of the density function at k.

4. Feb 25, 2013

### jwatts

false P(X=k) for any density function is 0. The probability density function tells you the probability that the experiment ends up in some interval. For instance, the PDF will tell you how likely it is that you find someone between 5 feet and 6 feet, if you use the normal curve perhaps. It won't tell you the probability that someone is exactly 6 foot. Only discrete random variables give you non zero probabilities for a single number. The CDF gives you the probability that all the previous values were reached, up to , and including the value you want. So for instance, let's say that you want to know, on the normal curve perhaps, the probability that a person is AT MOST 8 foot. then you would sum up all the previous probabilities up to the 8 foot mark. That will give you the probability that someone is under 8 feet tall.

Mathematically f(x)= density function F(x) = cumulative fucntion (d/dx)F(x)=f(x) or F(x)= the integral of f(x)

5. Feb 26, 2013

### Stephen Tashi

That might depend on the terminology used in particular textbooks. For "discrete" random variables P(X=k) need not be zero. From an advanced (measure theoretic) point of view the summation used to define the cumulative distribution function of a discrete random variable can be regarded as a type of integration. From that point of view, one may speak of the pdf and cdf of a discrete random variable. In elementary textbooks, the author may reserve the terms cdf and pdf for "continuous" random variables. If an author does this, I wonder what terminology he uses for the analgous functions associated with discrete random variables.