# 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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### Prove $S_k$ is a stopping based on $A$ being previsible

Probability with Martingales: It looks like we have a filtered probability space $(\Omega, \mathscr F, \{\mathscr F_n\}_{n \in \mathbb N}, \mathbb P)$ where $A = \{A_n\}_{n \in \mathbb N}$ ...
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### scotts theorem and other representation theorems for order aggreeing qualitative quantitative probability measures

Scotts theorem and other theorems give conditions under which a qualitative ordering (>= for at least as probable than) which satisfies certain constraints (total pre-order, finite cancellation axioms ...
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### Convergence in distribution: constant multiplication

If I have $$X_n/\sigma$$ converging in distribution to $\mathcal{N}(0,\sigma^2)$, does this mean I can just multiply through with $\sigma$ and obtain that $X_n$ converges to a standard normal? I ...
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### Monty Hall Problem Intuition

I was thinking about the Monty Hall problem and I thought of a possible intuitive explanation: You choose a door. Monty gives you the option of sticking with your original choice or instead ...
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### finding Expected Value for a system with N events all having exponential distribution

We have a system in which events happen one after each other. The time interval between each two events shown by random variable $t_i$. So, the time interval between the first and the second events is ...
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### Finding the density for $\min\{X, Y\}$

Problem: Let $X$ and $Y$ be independent and suppose that each has a $\text{Uniform}(0,1)$ distribution. Let $Z = \min\{X, Y\}$. Find the density $f_Z(z)$ for $Z$. Hint: It might be easier to first ...
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### Poisson Coin Flipping Problem

A problem from All of Statistics pg. 45: Let $N \sim \text{Poisson}(\lambda)$ and suppose we toss a coin $N$ times. Let $X$ and $Y$ be the number of heads and tails. Show that $X$ and $Y$ are ...
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### Joint pdf of X and Y with absolute value

Question. Joint probability function of continuous probability X, Y is here : $f_{X,Y}(x,y) = k(|x|-|y|) \ \ \ \ \ \ \ \ \ \ (-1< y< x< 2)$ Then what is k? I mean how can I differentiate ...
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