pooling - How to calculate pooled variance of two or more groups …
The variance of the first group is $\sigma_m^2$ and the variance of the second group is $\sigma^2_n$. The elements themselves are assumed to be unknown but I know the means $\mu_m$ and $\mu_n$. Is there a way to calculate the combined variance $\sigma^2_{(m+n)}$? The variance doesn't have to be unbiased so denominator is $(m+n)$ and not $(m+n-1)$.
Derive Variance of regression coefficient in simple linear regression
$\begingroup$ Yes, your formula from matrix notation is correct. Looking at the formula in question, $1-\frac1{n}\,=\,\frac{n-1}{n}$ so it rather looks as if you might used a sample standard deviation somewhere instead of a population standard deviation? Without seeing the derivation it's hard to say any more. $\endgroup$ –
What is the difference between N and N-1 in calculating …
But imagine now that you somehow know the true population mean, but want to estimate variance from the sample. Then you will substitute that true mean into the formula for variance and apply denominator N: no "-1" is needed here since you know the true mean, you didn't estimate it from this same sample.
Finding the Mean and Variance from PDF - Cross Validated
2015年1月15日 · You can solve for the mean and the variance anyway. See, for example, mean and variance for a binomial (use summation instead of integrals for discrete random variables). If you can't solve this after reading this, please edit your question showing us where you got stuck.
Var(XY), if X and Y are independent random variables
2019年3月16日 · Variance of product of multiple independent random variables (1 answer) Closed 5 years ago . if X and Y are independent Random variable then what is the variance of XY?
Variance of product of dependent variables - Cross Validated
Formula for the variance of the product of two random variables. 0. Relation between Variance of one ...
How do I calculate the variance of the OLS estimator
I believe this all works because since we provided that $\bar{u}$ and $\hat{\beta_1} - \beta_1$ are uncorrelated, the covariance between them is zero, so the variance of the sum is the sum of the variance. $\beta_0$ is just a constant, so it drops out, as does $\beta_1$ later in the calculations.
The linearity of variance - Cross Validated
2015年12月4日 · The more general formula for the variance of a sum of two random variables is $$\Var(X+Y) = \Var(X) + \Var(Y) + 2 \Cov(X,Y)$$ In particular, $\Cov(X,X) = \Var(X)$, so $$\Var(X+X) = \Var(X) + \Var(X) + 2\Var(X) = 4\Var(X)$$ which is the same as you would have deduced from applying the rule $$\Var(aX) = a^2 \Var(X) \implies \Var(2X) = 4\Var(X)$$
Calculate the variance from variances - Cross Validated
2020年8月14日 · For each group I do have available the mean and the variance. How can I calculate the mean and the variance from the total population? For the mean that should be easy: It is simply the mean of the means. But how about the variance? Edit: How to calculate the variance of a partition of variables seem to deal with a similar issue.
Variance of a stationary AR (2) model - Cross Validated
2017年1月16日 · Variance. If the process is stationary, we can write the covariance as a function of increment alone, so let the covariance function $\gamma(k) \doteq E[y_t y_{t+k}]$. We can find the variance $\gamma(0)$ by squaring and taking the expectation of both sides of equation $(*)$ with the following result