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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: $s^2 = \frac{1}{n} \sum_{i=... 1answer 9k views What is the difference between Mean Squared Deviation and Variance? I am doing some tutoring for an AS-Level maths student and unfortunately for me they are doing statistics. This is not my strong point, mainly from the point of view of remembering all of the ... 0answers 141 views What is the expected value of sample variance in this problem? Let$x_1,x_2,..x_{21}$be a random sample from a distribution having variance 5. Let $$\bar X = \frac1{21}\sum_{i=1}^{21}X_i\quad\text{and}\quad S=\frac1{21}\sum_{i=1}^{21}(X_i-\bar X)^2$$ What is ... 2answers 1k views 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 ... 1answer 8k views why sample variance has has n-1 in the denominator? [duplicate] Sample variance is calculated according to:$s^2=\frac{\sum{(x-\bar{x})^2}}{n-1}$Population variance is calculated according to:$\sigma^2=\frac{\sum{(x-\mu)^2}}{n}$Why denominator for sample ... 3answers 8k views 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 ... 2answers 2k views 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 ... 2answers 162 views 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 ... 1answer 68 views Is my work correct (easy problem, confidence intervals) The r.v.$X$represents the time taken by a computer in company$1$in order to perform a certain job, and$Y$represents the same thing but for company$2$. A sample of$n_X = 12$computers are taken ... 0answers 664 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: ... 2answers 134 views Definition of a sample: can it include the same object twice? 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 ... 0answers 79 views What is the estimate of sample mean variance? [duplicate] Possible Duplicate: How does the standard error work? What is the estimate of sample mean variance and how do you get it? Are my understandings of the following correct?$var(Y)=\frac{1}{N} \sum ...

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