Question

What is the difference between a pdf and a cdf? How are they related?

Explain this as you would to someone who wasn't in class when I did. Assume they have taken Calculus 2. You can use text, pictures, a video, a dance, a song... whatever you want. Be creative! Submit your explanation as one file (a pdf for text or image, a single video or audio file etc.)

Answer 1

Answer :

Pdf or probability density function is the function that describes how the probability is distributed over the given domain of data. That is it defines that probability that a outcome equal to some value. For example , let the pdf be f(x), it describes the probability that outcome take some value x. Suppose it's domain is natural numbers that is from 1 to +infinity.

Probability that x=3 => f(3)

Similarly P(x=10) = f(10). And so on.

One important thing here is sum of the pdf f(x) , for all given values of x in the domain is equals to 1.

Cdf : cumulative density function is the modified function generated using the pdf. It describes the probability of taking a value equals to or less than that particular value.

For example let cdf be F(x), it gives probability of taking a blue equals to or less than x.

F(3) = P(x<=3) = P(1) +P(2) + P(3) //assuming same function as above for pdf

So F(3) = f(1) + f(2) + f(3)

Small f denote pdf and capital F denote cdf.

Cdf(x) = sum of all pdf for all values less than or equal to x.