# Tagged Questions

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### Two-dimensional distribution and related variance computation

I have a simple statistical question (forgive me if I use statistical terminology in a wrong way) Suppose I have a random vector with two components, $(x_1, x_2)$, where $x_1$ can take values from $1$ ...
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### Estimating the population variance [duplicate]

I'm trying to understand the emphasized phrase in the following passage: The usual method of determining the probability that the mean of the population lies within a given distance of the mean of ...
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### method of moments with variance=$\sigma^2$

I am trying to estimate the value of a parameter by equating variance from a distribution to the sample variance... i.e. using method of moments estimation. Would it better to use the variance formula ...
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### Where did this risk exposure 'estimation-formula' come from?

I was reading a book and the authors metioned that risk exposure can be estimated scientifically using this forumula: $risk(\$) = \frac{(a + 4m + b)}{6}$and standard deviation$\sigma = ...
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### Mean and standard deviation of Gaussian Distribution

I have some random numbers which are generated from Gaussian Distribution. But I don't know the mean, standard deviation of that distribution. How can I find them using random numbers?
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### If I take n-standard deviations of my data what would be my confidence level with the estimate?

I have some measurement data of estimates vs actuals (of some metric $m$). For every such data I also have the ratio of $\frac{actuals}{estimates} = r \space (say)$ - if this ratio is greater than 1 ...
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### Estimating the functional form of the slowly time-varying variance of a Gaussian process

Consider the following simple set-up. In the interval $[0, 1]$ we are observing the realizations of independent normally distributed random variables at times $t_1,\ldots, t_N$. The r.v. $X(t)$ has ...
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### Why is sample standard deviation a biased estimator of $\sigma$?

According to the Wikipedia article on unbiased estimation of standard deviation the sample SD $$s = \sqrt{\frac{1}{n-1} \sum_{i=1}^n (x_i - \overline{x})^2}$$ is a biased estimator of the SD of the ...