# Questions tagged [sampling-distribution]

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### Why do we assume samples have the same variance when deriving standard error? [closed]

In all derivations I've seen of the standard error formula $\sigma/\sqrt{n}$, it is assumed all the samples in the sampling distribution have the same variance ($\sigma^2$). Why is it assumed they all ...
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### Linear Regression - Proof that coefficients estimated via OLS follow a normal distribution [duplicate]

The aim of my question can be better illustrated by this quote extracted from the third chapter of Elements of Statistical Learning (link to book): I'm trying to understand why, given that the error ...
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### Sample covariance of t distribution and degree of freedom

If $X$ is a P by N size matrix, $X_{ij} \sim N(0,\sigma_i^2)$ if I standardize this X matrix with sample mean and sample variance (assuming I don't have access to the population mean and variance) I ...
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### Do the 2.5th and 97.5th percentile of the theoretical sampling distribution of a statistic always contain the true population parameter?

I am trying to understand the validity of bootstrap percentile confidence intervals and I have stumbled on the following from these slides: Suppose we want to set a 95% confidence interval on $θ$, ...
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### Calculating the probability my observation, $Y_i$, is drawn from a random variable $X$?

If I sample a population distribution 2,000 times and get an estimator for the population mean, $\mu$, and the standard deviation, $\sigma$, how can I use these to get the probability that an ...
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### degrees of freedom in a t-test in Kruschke's BEST paper

This question is based on a comment by John Kruschke in his BEST paper, pages 589-590. Kruschke, John K. "Bayesian estimation supersedes the t test." Journal of Experimental Psychology: ...
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### Question about the conceptual sampling distribution for one time events

in this paper: Do Political Protests Matter? Evidence from the Tea Party Movement*, the authors use rainfall on the day of the tea party protests as a source of plausibly exogenous variation in rally ...
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### right skewed sample does not lead to normally shaped sampling distributions

I will provide R code for a reproducible example. I am calculating the difference in means for two groups. I get a sampling distribution by permutations but instead of a normally shaped distribution ...
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### Sampling distribution of the mean of the discrete-power law distribution

For a certain problem I wish to generate random integers $k$ so that their distribution follows $p_k \sim k^{-\alpha}$ for $k \geq k_{\text{min}}$, $k_{\text{min}} > 0$. I am following the ...
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### Sampling distribution of the mean of a Beta

Say we have $X \sim \text{Beta}(\alpha, \beta)$. What's the sampling distribution of its sample mean? In other words, what distribution does the sample mean $\bar{X}$ of a Beta follow?
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### Proof that the sampling distribution of the sample variance from $N(0,1)\sim \chi_{n-1}^2$
I'm reviewing old exams in preparation for a statistics final, and I'm stuck on a particular question: Suppose that you have n independent random variables $Y_i$, with each distributed normal with ...