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Results tagged with probability-distributions
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user 5963
In probability and statistics, a probability distribution assigns a probability to each measurable subset of the possible outcomes of a random experiment, survey, or procedure of statistical inference.
8
votes
What is the maximum entropy distribution on the natural numbers?
This follows (modulo any minor technical details I haven't checked) from the theory of exponential families. The main result there says that the distribution which maximizes entropy subject to constr …
- 8,501
5
votes
Finding joint probability from double marginals
No, the condition on the marginals is not sufficient. Consider for example three 0-1 valued random variables with bivariate marginals $p_i(s,t) = 0.5(1-\delta(s,t))$ for all $i, s, t$. The necessary …
- 8,501
3
votes
Accepted
Moment matching on the standard simplex
It is a standard result that the matrices of the form $\mu^{\otimes 2}$ for nonzero $\mu$ are the extreme rays of the positive semidefinite cone. That is to say, your condition on the second moments …
- 8,501
3
votes
Accepted
Joint probability distribution as functions
No. Here is a counterexample. Let $\mathcal{A} = \{1,2,3,4\}$, $\mathcal{B} = \{1,2\}$, and $f(x) = g(x) = \lceil\frac{x}{2}\rceil$. Let the joint probability mass function of $X$ and $Y$ be given …
- 8,501
1
vote
A sampling and learning question
The oracle produces i.i.d. samples from a fixed one of $n$ distributions $P_b$ corresponding to the $n$ possible values of $b$. The maximum likelihood estimator of $b$ is then the value that minimize …
- 8,501