What exactly is the difference bet. a CDF and a PDF?

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SUMMARY

The discussion clarifies the relationship between Probability Density Function (PDF) and Cumulative Distribution Function (CDF), emphasizing that PDF is the derivative of CDF, while CDF is the integral of PDF. It highlights that PDF provides a formula to describe probabilities for specific outcomes, such as calculating the probability of obtaining exactly 3 heads in 1000 coin tosses using the binomial distribution formula P(X=3)= 1000C3(1/2)³(1/2)¹⁰⁰⁰⁻³. The conversation also distinguishes between simple probability and PDF, noting that PDF is particularly useful for continuous distributions, while simple probability applies to discrete events.

PREREQUISITES
  • Understanding of Probability Theory
  • Familiarity with Cumulative Distribution Functions (CDF)
  • Knowledge of Probability Density Functions (PDF)
  • Basic concepts of Binomial Distribution
NEXT STEPS
  • Study the properties of Cumulative Distribution Functions (CDF)
  • Learn about Probability Density Functions (PDF) in continuous distributions
  • Explore the Binomial Distribution and its applications
  • Investigate the differences between discrete and continuous probability distributions
USEFUL FOR

Students in statistics, data analysts, and anyone seeking to deepen their understanding of probability theory, particularly in distinguishing between PDF, CDF, and simple probability concepts.

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Homework Statement



I understand that PDF is a derivative of CDF and hence CDF is the integral of PDF. But I don't understand the difference between PDF and simply probability? What exactly is the differece? What extra things does PDF tell us which simple probability does not?

Homework Equations



For example, we toss a coin and a head comes. Probability of it is 1/2. What's PDF in this case?

The Attempt at a Solution

 
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Well say you toss a coin 1000 times and you want the probability of exactly 3 heads. To write down all the possibilities, would take a long time. The pdf is basically a single formula that would describe the probabilities. So for the coin toss (it follows a binomial distribution)
P(X=3)= 1000C3(1/2)3(1/2)1000-3

A cdf sums the probabilities.


EDIT: that is for a discrete distribution
 
Last edited:
I think I'm getting to the idea but I'm not completely clear yet. I understand the difference between CDF and PDF but what's the difference between simple probability and PDF?

And do we always follow the binomial distribution in PDF?
 

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