# Questions tagged [law-of-large-numbers]

Several theorems stating that sample mean converges to the expected value as $n\to\infty$. There is a weak law and a strong law of large numbers.

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### Law of Large Numbers

Suppose X is uniform discrete distribution from a set of (1,2,3,...,m). How do i investigate the law of large numbers for this? I thought of doing this by maybe setting m as 10 and having sample of ...
1 vote
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### Is there a law or concept related to unchanging average?

I have a survey comprising 30 questions with 50k respondents where respondents mark each answer on a 5 point scale. An average of all the questions for all the respondents is metric we track monthly. ...
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1 vote
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### Weak Law of Large Number to Central Limit Theorem [closed]

Consider a distribution with unknown mean μ and population standard deviation σ=30. Using the Weak Law of Large Numbers, what is the minimum sample size in order to attain a probability of at least 99%...
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• 31k
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### Linear regression with one generated regressor

Suppose I have the regression model: $Y_i=T^{\top}_{i}\beta_0+e_{i}$ with $E(e_i|X_i)=0$, where we have two regressors $X_i,\ E(D|X_{i})$ so that $T^{\top}_{i}=[X_i,\ E(D|X_{i})]$. $X_{i}$ is a ...
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### Can someone provide a proof for this theorem that was used in the proof of law of large number?

Let $X_1,X_2,X_3,...$ be $i.i.d.$ with finite mean $\mu$. Then let $Y_i=X_i1_{\{|X_i|<i\}}$ There will be only finitely many terms such that $Y_i\neq X_i$ While that lecture notes did not ...
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### Showing the weak law of large number of non-IID sequence of random variables

Common proofs on the law of large numbers usually assume a sequence of IID random variables. If $X_1\dots X_n$ has a common expected value $\mu$, finite but not necessarily common variance (hence not ...
• 873
1 vote
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### Should bootstrapping and collecting sample means from a series of binomial distributions result in standard normal?

I’m trying to better understand several statistical concepts (bootstrapping, central limit theorem, and confidence intervals) by applying them to a binomial distribution (you can think of it as a coin ...
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### Why do typical sequences have probabilities $\sim2^{-nH(p)}$?

I've been reading a bit about typical sequences (in particular from these notes (pdf alert), pages 3 and 4). Let us focus on the case of binary sequences for simplicity. As far as I understand the ...
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### Law of Large Numbers

How do i proceed with this? any hints would help
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### Posterior mean with MCMC

Let's say we have a posterior distribution: $$\pi(\theta_1, \theta_2, \theta_3 | \bf{y})$$ and that we've run an MCMC algorithm to approximate this distribution. I know that there is a Markov chain ...
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### Expectation of 500 coin flips after 500 realizations

I was hoping someone could provide clarity surrounding the following scenario. You are asked "What is the expected number of observed heads and tails if you flip a fair coin 1000 times". Knowing that ...
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I was reading about conditional variance in Wikipedia and then the following property showed up $$E[V[Y \mid X]]=E[(Y-f(X))^2]-E[(E[Y \mid X]-f(X))^2]$$ Which i interpret as an irreducible error, ...