Cumulative Distribution Function

Created
Created
2023 Mar 7 2:33
Editor
Creator
Creator
Seonglae Cho
Edited
Edited
2025 Apr 29 0:0

CDF

For functions like min, you can first find the CDF using probability intervals and then differentiate it to get the PDF.
  • If two probability distributions have the same CDF, they’re the same
  • Two distinct probability distributions can’t have the same CDF, if two probability distributions have the same CDF, they’re the same.
    Inverse transform sampling
Random Variable X follows the probability distribution, then input into , results in a uniform
 
 

Proof that CDF is monotonic increase

Let , then , since and since it is a
Probability Density Function
 
 
 
 
 

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