Linked Questions

0
votes
3answers
162 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=...
3
votes
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 ...
1
vote
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 ...
11
votes
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 ...
1
vote
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 ...
0
votes
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 ...
2
votes
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 ...
6
votes
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 ...
3
votes
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 ...
1
vote
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: ...
5
votes
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 ...
0
votes
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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