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### 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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...