PDF and CDF in statistics

Probability density function(PDF)

Definition
PDF is a mathematical function. To map the possible outcomes of a random variable to their probabilities of occurrence, PDF is used. Let consider a function f(x) to be a probability function and this f(x) will lie between the maximum value a and minimum value b. You can imagine that [a,b] as the interval.
Formula: P(a<= x <=b)=∫_a^b f(x) dx.
Here,
Lowe limit =a
Upper limit=b

To integrate the given function for x with the lower limit a and upper limit b.

The output is called probability value. f(x) will be called PDF if the output/result of the the formula is equal to 1.

Properties:
1. f(x)>=0. It means that the value of function x should be greater than Zero.
2. When you integrate f(x) with respect to x in a range then the output should be always one.

Cumulative distribution function(CDF)

The cumulative distribution function of a random variable "X" is the probability that the random variable "X" takes a value less than or equal to x.
Formula:
f_X(x)=PC(X<=x)

Properties:
1. CDF can be defined for continuous random variables as well as discrete random variables.
2. Value lies between 0<=f_X(x)<=1
3. When value should 0 and 1,
f_x(-∞)=0
and,
f_x(∞)=1
4. f_X(x₁)<=f_X(x₂)
5. CDF is a monotone non-decreasing function.