Linked Questions

0
votes
3answers
792 views

What is the importance of the concept of probability space? [duplicate]

We know sample space (S), elementary outcomes and events. And axiomatically define probability of these events or assign probabilities to these events. Now event space (F) and the triplet ...
2
votes
0answers
38 views

General Questions on Measure Theory [duplicate]

The notion I have received while trying to study Measure theory that it is helpful when we move from discrete domain to continuous domain because in discrete domain we can count individual entities ...
1
vote
0answers
31 views

Continuous vs Discrete Distributions [duplicate]

In a discrete space, everything is centered around the function "P". Every event has a probability associated with it, and random variables simply map outcomes to numbers. P(X = x) is basically just a ...
23
votes
4answers
5k views

Can anyone clarify the concept of a “sum of random variables”

In my probability class the terms "sums of random variables" is constantly used. However, I'm stuck on what exactly that means? Are we talking about the sum of a bunch of realizations from a random ...
9
votes
5answers
3k views

Why is the sum of probabilities in a continuous uniform distribution not infinity?

The probability density function of a uniform distribution (continuous) is shown above. The area under the curve is 1 - which makes sense since the sum of all the probabilities in a probability ...
21
votes
2answers
2k views

Is there a statistical application that requires strong consistency?

I was wondering if someone knows or if there exists an application in statistics in which strong consistency of an estimator is required instead of weak consistency. That is, strong consistency is ...
5
votes
1answer
2k views

Definition of sample space

From Rohatgi-Saleh's book on probability and statistics: Def: The sample space of a statistical experiment is a pair $(\Omega,\mathcal S)$, where (a) $\Omega$ is the set of all possible outcomes of ...
10
votes
2answers
386 views

What is a probability distribution? [duplicate]

This is a very basic question, and maybe a silly one, but I'm struggling to understand the actual definition of a probability distribution. In Wasserman's "All of Statistics", for example, he says ...
1
vote
3answers
56 views

is probability defined on outcomes or events (or both)?

studying myself and trying to understand probability foundations, and I find that even books do not agree, or probably I do not understand. What I have learned: Outcome: what can happen in an ...
0
votes
0answers
57 views

Explain the descriptive statistics notion of population (distribution) to a measure theorist

My understanding of probability theory is a rigorous measure-theoretic one and I know almost nothing about descriptive statistics. However, I need to understand some of the commonly used notions in ...
1
vote
0answers
56 views

How to construct a Probability Mass Function from a sample of data

In decision tree learning, specifically when calculating Gini impurity, I understand that probabilities are assigned to a class label based on the node label proportions, such as, ...