# Tagged Questions

Use this tag only if your question is about the modern theoretical footing for probability, for example probability spaces, random variables, law of large numbers, and central limit theorems. Use [tag:probability] instead for specific problems and explicit computations. Use [tag:probability-...

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### An independent squence of functions that are uniform on $[0,1]$

Suppose that $X$ is uniform in $[0,1]$. Find an infinite sequence of functions $f_{i}$ so that all $f_{i}(X)$ are independent and uniform $[0,1]$. um I'm not really sure how to do this. I'm thinking ...
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### Proof for k-connectedness of random graphs

I am really new to the theory of random graphs. It seems a lot of articles take for granted that: For $k\in\mathbb{N}\setminus\{0\}$ and $p\in(0,1)$ fixed, almost every graph in $G(n,p)$ is $k$-...
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### If $P$ a probability of a sentence to be true, then $\{P(\phi | T_i)\}_{i \in \mathbb{N}}$ is a martingale over constructed theories $T_i$

I am reading Section 2.1 of Definability of Truth in Probabilistic Logic. For a language $L$, fix a probability distribution $P:L \to [0,1]$. Enumerate sentences $\phi_1, \phi_2, \ldots$ of a ...
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### What is the transformation that maps a Gaussian distribution to a Beta distribution?

Suppose X is a random variable with Gaussian distribution over domain $\mathbb{R} = (-\infty, +\infty)$, with PDF function $f_X$. And Y is a random variable with Beta distribution over domain $[0,1]$,...
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### Equivalence of $\sigma$-algebras: generated by $[a,b]$ and $(-\infty,b]$

Show that the $\sigma$-algebras generated by the collection of all intervals of the form $[a,b]\subset\Bbb R$ and by the collection of all the intervals of the form $(-\infty,b]\subset\Bbb R$ are ...
For a normal random walk where $Y_i = \pm\frac{1}{2}$ with equal probability and $X_i = \sum_{i=1}^n Y_i$, my book says the $\sigma$-algebra generated by a martingale is written as \$\sigma(X_0, X_1, ...