# 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 exercise about changing the measure and convergence in $L^1$

this is exercise 17.12 from probability essentials written by jacod & protter. Suppose $lim_{n→∞} X_n = X$ a.s. Let $Y = sup_n |X_n − X|$. Show $Y < ∞$ a.s. , and define a new probability ...
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### Combinatorics-Summation doubt in the proof of the expectation of the Hypergeometric distribution.

The proof starts considering this equality: $(d/dx (1+x)^A)(1+x)^B = A(1+x)^{A+B-1}$ Then it keep on changing every $(1+x)^{A or B}$ for its binomial coefficient. That 's what I don't understand. If ...
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### Squared Hellinger Distance subadditive for Product measures

How can I show that the squared Hellinger Distance is subadditive for Product measures? We have $\mathbb{P} = \otimes_{i=1}^n \mathbb{P_i}$ and $\mathbb{Q} = \otimes_{i=1}^n \mathbb{Q_i}$ ...
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### How to use Bayes's rule with mixed distributions?

On page 81 of The Likelihood Principle by Berger and Wolpert (1988) I find the following claim (which references example 20 on page 75). We consider a certain statistical problem from a Bayesian ...
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### Time taken to give answer if probability is given.

This is a question that I am struggling with: Since the password is periodically changed, you would like to know the answer as soon as possible. So you decide to interrogate the minions in an order ...
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### Probability of Independent Events individual vs in series

I understand that independent events (such as a fair coin flip) should not be viewed in succession. For example, if you flip heads 10 times in a row, the odds of flipping the next coin heads is still ...
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### Questions on Kolmogorov Zero-One Law Proof in Williams

Here is the proof of the Kolmogorov Zero-One Law and the lemmas used to prove it in Williams' Probability book: Here are my questions: Why exactly are $\mathfrak{K}_{\infty}$ and $\mathfrak{T}$...
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### Convergence in distribution of distributions $p_n$ implies convergence in distribution of $s_n$?

Question Setup Suppose $p_n(x,y)$ is a sequence of probability densities on $\mathbb R^2$ and $q_n(x)$ is a sequence of densities on $\mathbb R$ such that \begin{align*} \int b(x,y) \ p_n(x,y) \ dx ...
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### Countable infinite support of probabilistic measure

Let $E\subset\Omega$ be a countable infinite set. I want to define probability measure $p$ on $\Omega$, such that $p(x)>0 \iff x\in E$ and all $x\in E$ have the same probability. Is that possible? ...
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### Consequence of random walk with positive speed on a graph

Consider a random walk $X(n)$ on a vertex-transitive graph where the random walk has positive speed, i.e., $$\lim\limits_{n \rightarrow \infty} \frac{d(X(n), X(0))}{n}= \alpha>0$$ almost surely. ...
Can somebody help me proving that the following hitting time is a stopping time? Let $\{X_t\}_{t\ge 0}$ be a real-valued, right-continuous process, adapted to a filtration $\mathfrak{F}$ which ...