Probability Mass Function vs Probability Measure

AI Thread Summary
A probability mass function (PMF) is specifically used for discrete distributions, such as the binomial distribution, while a probability density function (PDF) is used for continuous distributions like the Gaussian. The term 'probability measure' describes a function that assigns probabilities to events within a sample space, applicable to both discrete and continuous distributions. Although PMFs and probability measures are related, they are not the same; PMFs are a specific type of probability measure for discrete cases. Understanding these distinctions is crucial for proper application in statistical analysis.
blahblah8724
Messages
31
Reaction score
0
What is the difference between a probability mass function and a probability measure or are they just the same thing?

Thanks!
 
Physics news on Phys.org
Essentially the same. There might be subtle differences due to context.
 
blahblah8724 said:
What is the difference between a probability mass function and a probability measure or are they just the same thing?

Thanks!

The 'probability mass function' (PMF) applies to discrete distributions like the binomial. For continuous distributions like the Gaussian, the term 'probability density function' (PDF) applies. The term 'probability measure' refers to a function which maps from an event space to the interval [0,1] and can apply to either kind of distribution.
 
Last edited:

Thread 'Deductive proof in logic formal systems'

I was reading documentation about the soundness and completeness of logic formal systems. Consider the following $$\vdash_S \phi$$ where ##S## is the proof-system making part the formal system and ##\phi## is a wff (well formed formula) of the formal language. Note the blank on left of the turnstile symbol ##\vdash_S##, as far as I can tell it actually represents the empty set. So what does it mean ? I guess it actually means ##\phi## is a theorem of the formal system, i.e. there is a...
View full post »

Similar threads

I On transformation of r.v.s. and sigma-finite measures
Replies
1
Views
2K
I Basic Probability Theory Question about Lebesgue measure
Replies
14
Views
2K
I Are different interpretations of probability equivalent?
Replies
25
Views
3K
A Probability Density Function: Converting Experimental Observations to PDF
Replies
4
Views
2K
A Research about chained functions
Replies
2
Views
2K
  • Sticky
Insights Frequentist vs Bayesian Probability: What's the Difference?
Replies
44
Views
12K
A Concrete examples of randomness in math vs. probability theory
Replies
11
Views
3K
B Is an Ensemble of Measurements a True Reflection of Probability?
Replies
1
Views
1K
I Sample space, outcome, event, random variable, probability...
Replies
6
Views
3K
A The name of this probability density function
Replies
4
Views
1K

Hot Threads

Recent Insights

Back
Top