# Tagged Questions

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### What coefficient could I use to calculate the relative difficulty of a test in relation to others using only mean and population standard deviation?

I have a series of tests, all of them of different difficulty, and from each of them I get an average score and a population standard deviation; e.g: ...
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### Compute the variance of parameter estimates given limited number of samples

I'd like to infer the variance of estimated parameter $\hat\theta$ of the density function of $f(x;\theta)$ given only a limited number of samples $X_1,\cdots,X_n$. Bootstrapping doesn't perform well ...
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### Finding the UMVUE of the variance of a gaussian with mean zero

Given $Z_1, ..., Z_n, \sim\mathcal{N}(0, θ^2), θ>0$. Define $X_i=|Z_i|$ and consider estimation of $\theta$ and $θ^2$ on the basis of the random sample $X_1,...X_n$. Find the uniformly minimum ...
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### Bias correction in weighted variance

For unweighted variance $$\text{Var}(X):=\frac{1}{n}\sum_i(x_i - \mu)^2$$ there exists the bias corrected sample variance, when the mean was estimated from the same data: ...
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### Maximum of sample variance

Let $X_1, \dots, X_n$ be i.i.d from the interval $[0,1]$. I am interested in situation when the sample variance $$\frac{1}{n-1} \sum_{i=1}^n (X_i - \overline{X})^2$$ (where $\overline{X}$ is sample ...
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### How to compute variance of a continuous time sequence?

I am observing two continuous time-series where at every instant in time I may observe a unary event. That is, for each sequence, say $S_1$, I have a data set comprised of $S_1 = (t_0, t_1, ..., t_m)$ ...
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### Variance of the reciprocal II

Background I've recently read the paper Leo A. Goodman, On the Exact Variance of Products Journal of the American Statistical Association Vol. 55, No. 292 (Dec., 1960), pp. 708-713 from where I ...
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### Understanding variance estimators

I am having trouble understanding the following. Let $\mu$ and $\sigma^2$ be the true mean and variance, $\bar{x}$ and $s^2$ the measured mean and variance for a random variable $x$, where ...
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### Estimating the variance of poker win rates

Suppose you have a casino with n poker players. Each player has a win rate - the amount of money he wins or loses per hand. We assume that these win rates are normally distributed with a mean of 0. ...
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### Estimating variability of unseen factor

I'm looking at binomial data where I believe that the probability of the outcome is the product of two independent factors. If you think of it as a two step decision, At the first step, there is a ...
### Calculating $Var\left\{(\hat{m}-m)^2\right\}$ for a univariate normal distribution
Suppose $\hat{m} = \frac{1}{N}\sum_{i=1}^{N}(X_i)$ where $X_i \sim N(m,\sigma)$. Are the following steps correct? \$Var\left\{(\hat{m}-m)^2\right\} = E\left\{(\hat{m}-m)^4\right\} - ...