Questions tagged [probability]
For questions about probability. independence, total probability and conditional probability. For questions about the theoretical footing of probability use [tag:probability-theory]. For questions about specific probability distributions, use [tag:probability-distributions].
109,318 questions
-2 votes
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Best practice learning statistics and probability [closed]
I have the resource of statics and probability to learn and solve. My issue is that I know the theory and basic knowledge of math but hard time on statics and probability. Let my assume my self I am ...
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Function is continuous except on a set of null Wiener measure
Let $C$ the space of real continuous functions defined on $[0,1]$. With the topology induced by the uniform norm on $C$, let $\mathcal{C}$ the borelians induced by this topology. Let $\mathcal{B}$ the ...
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Modelling a dice game without straightforward computation
I'm trying to model the following rolling dice game: Start with one standard six-sided die and a fixed number of rolls, say n rolls. For each roll, we add the result to a running total. If the result ...
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3 votes
1 answer
56 views
Conditional probability for linear combinations of independent exponentials
I am working on the following exercise. Let $$X_1 \sim \mathrm{Exp}\left(\tfrac12\right), \qquad X_2 \sim \mathrm{Exp}\left(\tfrac12\right),$$ independent. Define $$Y_1 = X_1 + 2X_2, \qquad Y_2 = 2X_1 ...
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0 votes
2 answers
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Finding shape and scale parameters of Gamma distribution given a confidence interval
This would have been a comment on Munki's question about the same thing but I just created my account so I don't have enough rep. Suppose I have a confidence interval $(u, l)$ with respect to some ...
0 votes
0 answers
72 views
Probability of rolling a specified face for Archimedean solids
Here it is shown that (for a "suitable" mathematical definition of fairness) there are no fair $n$-sides die with odd $n$. The question originated with fairness being defined as, among other,...
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2 votes
0 answers
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An MLE Asymptotic Normality problem with i.n.i.d. data
Suppose $n \in \mathbb{N}$. Suppose $s_0 > 1$ and $\xi_j \sim N (0, j^{- s_0} + n^{- 1})$, $j = 1, 2, 3, \ldots, n$. Let $\hat{s}_n$ be the maximum likelihood estimator of $s_0$. Is $\hat{s}_n$ ...
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0 votes
1 answer
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Why does expectation project onto constant functions?
Let $X \in L^2$. Then $Z = E[X|G]$, for some sub $\sigma$-algebra $G$, is the orthogonal projection of $X$ onto $L^2(G)$. That is $Z$ is the random variable such that for every $G' \in G$: $$\int_{G'} ...
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