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How come the proportion of heads to tails across a large number of coin flips tend toward $1:1$ if all outcomes are equally likely?

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#probability #permutations #law-of-large-numbers
846
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S.N. Bernstein Law of Large Numbers

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#probability #probability-theory #law-of-large-numbers
50
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Convergence of a function of correlated random variables

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#convergence-divergence #asymptotics #uniform-convergence #weak-convergence #law-of-large-numbers
825
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Strong law of large numbers for function of random vector: can we apply it for a component only?

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#probability #expectation #law-of-large-numbers
1k
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Strong law of large numbers for the conditional expectation of functions of random vectors

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#probability #probability-theory #stochastic-processes #conditional-expectation #law-of-large-numbers
227
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Arithmetic average of random variable with infinite mean

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#probability #law-of-large-numbers #borel-cantelli-lemmas
720
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Almost sure convergence of a certain sequence of random variables

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#sequences-and-series #probability-theory #convergence-divergence #random-variables #law-of-large-numbers
54
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simplify with law of large numbers

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#probability-theory #expectation #law-of-large-numbers
316
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A question regarding strong law of large numbers cannot be verified by Borel canteli lemma

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#convergence-divergence #law-of-large-numbers #borel-cantelli-lemmas
65
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Problem on Central limit theorem and Law of large numbers

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#probability-theory #probability-distributions #central-limit-theorem #law-of-large-numbers
32
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Random coefficient GARCH(1,1): Existence of solution

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#statistics #convergence-divergence #stochastic-processes #time-series #law-of-large-numbers
219
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$X=\sum_{i=1}^{N}X_i$,estimator for $N$

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#statistics #statistical-inference #law-of-large-numbers
77
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$\frac 1n \sum_{k=c+1}^n X_k X_{k-c}$ converges a.s to $0$ when $X_n$ is i.i.d. with mean $0$.

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#probability-theory #independence #probability-limit-theorems #law-of-large-numbers
207
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Convergence in distribution using strong law of large numbers

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#probability-theory #probability-distributions #law-of-large-numbers
151
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A peculiar linear programming: random variables and limits

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#limits #random-variables #expectation #linear-programming #law-of-large-numbers

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