# Questions tagged [variance]

The expected squared deviation of a random variable from its mean; or, the average squared deviation of data about their mean.

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### How do you calculate variance for percentages?

I know this seems like a simple questions but I am trying to wrap my head around calculating variance for percentages (e.g. 15%, 16%). I know that 15% is equivalent to 0.15, but when I try to ...
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### What statistical method deals with a continous predictor characterized by low variance?

I would like to run a study in which my predictor is a continuous variable. I already know that the distribution is normal but most of the points fall close to the center. I think that small ...
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### How does pooling affect variance?

Suppose you are looking at the prevalence of a certain disease and you can detect this disease in fecal samples. How does having a bunch of pooled fecal samples (i.e., taking a fecal sample from 5 ...
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### How much will the variance change in this scenario?

Imagine that a firm decides to increase the salary of every single of its employees by 10% of their current salary. The average of the salaries will increase by 10% too. But, how will the variance of ...
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### Explanation for Bessel's correction [duplicate]

In textbooks and online the explanation for Bessel's correction is that the sample points are closer to the sample mean than the population mean.This is true for sampling with replacement as well. So, ...
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### Unbiased estimator for Variance

So basically I have a survey where for each unit 1, ..., N in the population, we flip a fair coin to decide whether this person will be included in the survey or not. Let S be the r.v. denoting the ...
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### Mean and variance of a function of random multivariate vector

Let's assume to have a scalar function $Y=f(X)$, that is function of a multivariate normally-distributed random variable $X\sim\mathcal{N}(\mu, \Sigma)$. Is there a general way to compute, even in an ...
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### Linear Mixed Effects Model Variances

Consider the following model: \begin{equation} Y_i = X_i\beta + Z_ib_i + \varepsilon_i, \end{equation} where $b_i \sim N(0, D)$, and $\varepsilon_i \sim N(0, R_i(\gamma))$. The variance of $Y_i$ ...
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### What conclusions can we draw from different correlations between IQ scores between subjects belonging in different groups?

I was reading a presentation where research was quoted according to which children and parents who live together have IQs that are correlated with a correlation coefficient of 0.42 while children and ...
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### Why do some people say that an asymptotically unbiased estimator “satisfies a strong law of large numbers”?

If $x\in\mathbb R$, an estimator for $x$ is an integrable random variable $X$. We say that $X$ is unbiased if $\operatorname{Bias}(x,X):=x-\operatorname E[X]=0$. Now, in the context of Markov chain ...
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### How to identify periods of high variance in temporal data [closed]

I have a dataset with concentration of a chemical (continuous) as the dependent variable plotted against time (continuous). I expect that certain periods during the year (e.g. summer) will have ...
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### Why do regression estimates provide lower relative error than averaged values?

I am trying to estimate the per-cell protein concentration for some samples. I have performed a series of protein extractions for each of my samples, with each extraction using an increased (and known)...
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### How can I compare the performance of two measurement modalities?

Let's say given some 3D images of the brain, I have two methodologies to measure the brain's volume. I'll call these two methodologies M1 ...
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### Mean and covariance of Bernouilli

I am given probability distribution here for a multinomial bernoulli: $p_{x}(x|z=j; \mu^{j}) = \prod^{d}_{i=1}(\mu^{j})^{x_{i}}(1-\mu^{j})^{1-x_{i}}$ where $x_{i}$ takes value 1 or 0, $\mu_{j}$ is ...
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### $X$ has distribution function $F(x) = e^{-e^{-x}}$. Justify that such a probability measure on $\mathbb{R}$ exists

How can I prove a probability measure exists? If $F(x) \rightarrow 1$ as $n \rightarrow +\infty$, does that mean $F(x)$ does exist? And how should I calculate $\mathbb{E}(F(X))$ and $Var(F(X))$?