Probability Distribution Function

It is divided into two parts Discrete Probability Distribution Function and Continuous Probability Distribution Function.

Discrete Probability Distribution Function: 

 Discrete means a variable that takes values from afinite or countable set, Lets say when we roll a dice we might get the value in between 1 to 6.

When we roll a dice the probability of getting each value is ⅙ as shown in the below table .

When we sum all the possibilities we will get one i.e  where f(X) and p(X) is a PDF.where f(X) and p(X=..) will be denoted as PDF.

Cumulative Distribution function( cumulative means addition of successive parts), means when we want to roll a dice for one the probability will be ⅙ when I want to roll a dice for 2 the probability will be either 1 or 2 so it is 2/6 and so on.

CDF will be defined as F(X) or P(X<=…)

Continuous Probability Distribution Function:  

        When values is continues like age,distance,time etc.. we can say it is continuous.

For example:

Discrete PDF we took a example of rolling a dice, the output after rolling will be either 1 or 2 or 3 or 4 or 5 or 6, means  finite or countable set.

continues PDF, lets say if I am waiting for a cab, it might take 1 min or 1.1 or 1.1232 or 2.1232 and will go on, means infinite or uncountable set.