Questions tagged [statistics]

Question 1

Suppose we have the sum of random, independent variables $$ Z_{ij} = X_i + Y_{ij}, $$ where $X_i \sim \text{Uniform}(-d, d)$ and $Y_{ij} \sim \text{Normal}(\mu, \sigma)$. Given that only one sample of ...

Question 2

I embarrassingly have a very simple question to ask in interpreting a data point. I have a calculated performance goal “event free rate” of 89%. I have an observed safety rate of 13.3% (95% CI: 8.5% - ...

Question 3

I have $n$ unit vectors $\mathbf{x}_i \in \mathbb{R}^p$, whose (sample) mean direction is calculated with $$ \mu = \frac{\bar{\mathbf{x}}}{\bar{R}}, \text{ where } \bar{\mathbf{x}} = \frac{1}{n} \...

Question 4

Given the linear regression model $$ Y = X\theta + \varepsilon, $$ the typical distribution of $\varepsilon$ is gaussian with mean zero and variance $\sigma^2$, but we could also assume $\varepsilon \...

Question 5

Yesterday I enjoyed some rounds of RISK: Global Domination with a friend from university. It is a long-running in-joke that “True Random” is the cause of winning and losing certain battles. Our ...

Question 6

I am grading hypothesis tests for an introductory statistics class and students occasionally give the following conclusion after rejecting the null hypothesis: Since $H_0$ is rejected, there is not ...

Question 7

Unbiased Variance Estimator Let $x_1 , \ldots, x_N$ be iid sampled from X. Let Y(N) denote the N-mean estimator given by $$ Y(N) = \frac{1}{N} \sum_{i=1}^N x_i $$ Let v(N) denote the unbiased N-...

Question 8

I was reading something. The context was we could measure the variables $X$ and $Y$ on individuals. And it appeared that $X$ and $Y$ were correlated with correlation: $\rho=0.3$. The writer then ...

Question 9

We know that if an i.i.d. sample is drawn from $p_{\theta}=\text{Ber}(\theta)$, $\theta\in (0,1)$ then $$\mathbb{E}_{p_{\theta}}[\bar{X}] = \theta,$$ where $\bar{X}$ denotes the sample mean. Now, ...

Question 10

This is a simple question from measure theory. Fix a measurable space $(E,\mathcal{E})$ and a family $(P_i)_{i\in I}$ of probability measures on $(E,\mathcal E)$ ($I$ is any non-empty set). Let $n\geq ...

Question 11

I am studying multi-class classification metrics and want to confirm the correct way to compute them from a confusion matrix. A weather classifier labels days as Sunny, Rainy, Cloudy. The test results ...

Question 12

Let $(X_n)_{n\in\mathbb N}$ be a sequence of independent random variables with the same distribution. The common distribution $\mu$ is such that it is symmetric, that is, $\mu((-\infty,x])=\mu([-x,\...

Question 13

Given a finite (multi)set of elements $\{x_1, \ldots, x_n\}$ the arithmetic mean $\mathsf{AM}$ is less than or equal to the maximum element call it $\max$. In otherwords, $\mathsf{AM} \leq \max$. But ...

Question 14

Say $E = \{p_\theta : p_\theta(x) = \exp(x^\top \theta - A(\theta)), \theta \in \Theta, M \theta = b\}$ is an exponential family affinely constrained in its natural parameter, where $\Theta$ is a ...

Question 15

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 $\hat{s}_n$ ...

Stack Exchange Network

Questions tagged [statistics]

What is probability distribution function of the sum of two independent random variables when one variable is correlated with itself?

Am I interpreting this data correctly? (Performance goals and confidence intervals) [closed]

Standard error of a mean direction

Error distribution of linear Regression

Finding an exact closed (non-recursive) form formula for the probabilities in a game of Risk

Double negatives in hypothesis test conclusions

Covariance of Unbiased Sample Variance Estimators with Overlapping Samples

Predicting $Y$ from a correlated variable $X$

Mixture Model Expectation

Dominated statistical models

Verifying One-vs-All Precision and Recall calculations from a multi-class confusion matrix

“Central limit theorem” for symmetric random variables with no finite mean

How much less is the arithmetic mean than the max given the average deviation?

Does online mirror descent between dually flat space converge to the global optimum

An MLE Asymptotic Normality problem with i.n.i.d. data

Hot Network Questions