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### What is the difference between Mean Squared Deviation and Variance?

I am doing some tutoring for an AS-Level maths student and unfortunately for me they are doing statistics. This is not my strong point, mainly from the point of view of remembering all of the ...
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### Estimating the covariance matrix in linear discriminant analysis

I was trying to derive the equations from page 109 in "elements of statistical learning" (image below) To be honest, I am not sure how the covariance $\Sigma$ is estimated (the third bullet point in ...
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### Measure the fluctuation of data

I have 2 series of data, for example: s1: 0.3 0.3 0.4 0.8 0.6 0.5 0.7 s2: 0.7 0.7 0.6 0.8 0.7 0.5 0.6 It's easy to see that ...
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### What value of $\alpha$ makes $\sum_{i=0}^n (x_i-\alpha)^2$ minimal?

I know that $\bar{x}$ makes absolute result of $\sum_{i=0}^n (x_i-\alpha)$ minimum. In fact it makes it zero. But how to find what value of $\alpha$ makes $\sum_{i=0}^n (x_i-\alpha)^2$ minimal? What ...
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### Expected number of successes from $N$ Bernoulli trials with different $p$

Suppose I have N probabilities $(p_1, p_2,...,p_N)$ that represent the chance that each that a corresponding test was passed. How do I apply the Bernoulli distribution to determine the expected number ...
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### Why does Restricted maximum likelihood yield a better (unbiased) estimate of the variance?

I'm reading Doug Bates' theory paper on R's lme4 package to better understand the nitty-gritty of mixed models, and came across an intriguing result that I'd like to understand better, about using ...
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When estimating parameters such as (I don't care about this specific instance particularly) Variance of a random variable X, one usually adopts Bessel's correction, i.e. using the formula $\hat{Var}{(... 0answers 650 views ### Estimation of variance: How to bring Bessel's correction together with degrees of freedom? I have been considering multiple textbooks to find out the reason that the denominator of the estimation of the population variance is n-1 rather than n. Depending on the book, two reasons are given: ... 1answer 138 views ### Why is$\frac{\sum^n_{i=1}(X_i-\bar{X})^2}{\sigma^2}$chi-square distributed with$n-1$degrees of freedom? On Wikipedia, it says If$X_{i};i=1,\ldots ,n$are independent normal$(\mu ,\sigma ^{2})$random variables, the statistic $$\frac{\sum\limits^n_{i=1}(X_i-\bar{X})^2}{\sigma^2}$$ ... 3answers 159 views ### Variance (different definitions) I'm new to statistics and reading stats books I found different definitions for Variance. Definition1:$ s^2 = \frac{1}{n-1} \sum_{i=1}^n (x_i - \bar{x})^2 $Definition2:$ s^2 = \frac{1}{n} \sum_{i=...
Wikipedia defines a sample as: a subset of a population. While exploring the reason why we divide by $(n-1)$ instead of $n$ when calculating standard deviation (discussed in this question), I came ...