Linked Questions

1
vote
1answer
157 views

Can there be a lottery of the natural numbers? [duplicate]

Can there be a lottery of the natural numbers, so that every natural number is chosen equally likely? The standard answer would be "No" because: If we define a measure $\mathbf{P}$ on $\mathbb{N}$ so ...
24
votes
9answers
5k views

Probability of selecting an even natural number from the set $\Bbb N$.

I confirmed on this thread that there are as many as even natural numbers as there are natural numbers. Question : Suppose I have selected a number $n \in \mathbb N$ , what is the probability that $...
10
votes
6answers
10k views

Probability of picking a random natural number

I randomly pick a natural number n. Assuming that I would have picked each number with the same probability, what was the probability for me to pick n before I did it?
27
votes
5answers
3k views

Card doubling paradox

Suppose there are two face down cards each with a positive real number and with one twice the other. Each card has value equal to its number. You are given one of the cards (with value $x$) and after ...
3
votes
2answers
2k views

What do we mean by rate in the exponential distribution?

When we talk about $X$ being a RV with an exponential distribution $$f(x)= 1-e^{-\theta x} \,\,\,\,\, \text{for}\,\,\,\ \theta>0$$ we say that it describes the time between two events in a Poisson ...
5
votes
4answers
171 views

Are Parabolas With Two x-Intercepts More Numerous Than Parabolas With No x-Intercepts?

Suppose we randomly assign values to a, b and c in the equation $y=ax^2 + bx + c$. Whenever the discriminant $(b^2-4ac)$ is positive, the parabola will have two x-intercepts. This will happen ...
7
votes
1answer
558 views

Krylov-Bogoliubov for measurable transformations

In the Krylov-Bogoliubov theorem, the transformation is assumed continuous. Does the theorem hold if the transformation is assumed only to be measurable? If not, what is a counterexample? Edit A few ...
6
votes
0answers
190 views

Is this fraction undefined? Infinite Probability Question.

Where $\frac{1}{\infty}$ and $\frac{\infty}{\infty}$ are both undefined terms that generally lead to nonsense, I'm wondering if we can assert that...: $$\frac{1+1+1+\cdots}{1+1+1+\cdots} = 1$$ ...or ...
0
votes
2answers
81 views

Uniform probability over real numbers?

I'm a bit conflicted by two answers I read. This first one, regarding the implications of different infinite cardinalities, explains that We often talk about a "uniform" probability over [0,1] ...
0
votes
3answers
45 views

Activation Function to [0,100]

I am looking for an activation function that squashes $\mathbb{R}$ to $[0,100]$. Currently I am using $$f(x) = \frac{100}{1+e^{-x}}$$ but this does not evenly distribute the values across the ...
1
vote
1answer
118 views

How is randomness quantified in Bayesian Statistics?

How is randomness quantified in Bayesian Statistics? In the finite case of N items, it is simple, since I can assign a probability of 1/N to each of the item. However, I wonder what happens if I want ...
1
vote
2answers
78 views

What's the probability that a particle jumps out of an interval?

Suppose I have a small particle and put it on the center of an interval on a 1-D axis. If the particle undergoes a motion that satisfies: It chooses its direction freely and randomly It ...
2
votes
0answers
39 views

What is the probability of choosing a interval B such that B is inside the interval A?

Let $I = [0,\ n],\ A = [a,\ b] : A \subseteq I$ Also, $0 \leq a \leq b \leq n$ and $a, b, n \in \mathbb{N}$. I'll choose a real value $x$ uniformly out of $I$. What is the probability of the ...